Algebra Class: Intercepts of Linear Equations

Questions and Answers

Find the x & y intercepts of $y=2x+4$

X intercept: (-2,0), Y intercept: (0,4)

What is a variable?

Letter that replaces an unknown quantity.

What is a constant?

Number by itself in an expression (no letter with it).

What is a coefficient?

Number multiplied by a variable (the 3 in 3x). Signup and view all the answers

What word means you have to switch the order of terms in a translation problem?

Than. Signup and view all the answers

What buttons do you push to clear a calculator?

2nd + 7 1 2 or 2nd + 7 all 2. Signup and view all the answers

What are the calculator keystrokes for changing a decimal to a fraction or for reducing a fraction?

Math enter enter. Signup and view all the answers

What do you have to put in the calculator when you plug in numbers for variables?

Parentheses. Signup and view all the answers

Are negative signs and subtraction signs interchangeable on the calculator?

False Signup and view all the answers

What operation is used for quotient?

Division. Signup and view all the answers

What operation is used for difference?

Subtraction. Signup and view all the answers

What operation is used for product?

Multiplication. Signup and view all the answers

What do you do when evaluating an expression that has a long fraction bar?

Solve the top, solve the bottom, then divide. Signup and view all the answers

How do you enter an exponent in the calculator?

^ (rooftop button). Signup and view all the answers

Any non-zero number raised to the zero power is what?

One. Signup and view all the answers

What are the steps for simplifying expressions?

Distribute, then combine like terms. Signup and view all the answers

What is the order of operations?

Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right. Signup and view all the answers

What two things must be the same to combine like terms?

Variable and exponents. Signup and view all the answers

What operation do we use to combine like terms?

Addition. Signup and view all the answers

If there is a variable with no number in front, what is the understood coefficient?

One. Signup and view all the answers

What do you write if two like terms cancel out when you combine them?

Nothing. Signup and view all the answers

Are constants like terms?

True Signup and view all the answers

What do you distribute if there is no number in front of the parentheses in the expression $2 - (x + 3)$?

Negative one. Signup and view all the answers

What is the goal when solving equations?

Get the variable by itself (isolate the variable). Signup and view all the answers

What are the steps for solving equations?

Distribute, combine, move +,-, isolate x,/ Signup and view all the answers

What are the steps for solving inequalities?

Distribute, combine, move, isolate the variable, flip, if necessary. Signup and view all the answers

What is the flip rule that is used with inequalities?

If you multiply or divide both sides by a negative number you flip the inequality sign. Signup and view all the answers

How do you know if you need an open or closed bubble when graphing inequalities?

< or > open bubble; ≤ or ≥ solid bubble. Signup and view all the answers

How do you determine if a graph is a function?

Vertical line test. Signup and view all the answers

How do you see if a table, list of points or mapping diagram is a function?

Check to see if the x repeats. Signup and view all the answers

What is domain?

Set of all x values. Signup and view all the answers

What is range?

Set of all y values. Signup and view all the answers

What do you look for on a table if you are looking for intercepts?

Look for the zeros. Signup and view all the answers

What is the zero of a function?

X intercept. Signup and view all the answers

What is the x value of every y intercept?

Zero (0,#). Signup and view all the answers

What is the y value of every x intercept?

Zero (#,0). Signup and view all the answers

How do you tell if a graph is linear?

It is a straight line. Signup and view all the answers

How do you tell if a table represents a linear function?

Plot the points and see if it is a straight line or look for a constant rate of change (slope). Signup and view all the answers

How do you tell if ordered pairs are a linear function?

Plot the points and see if the graph is a straight line. Signup and view all the answers

What do we use to find slope if we are given two ordered pairs?

Slope formula (or plot points and do rise over run) or use stat edit stat calc 4. Signup and view all the answers

What letter represents slope?

M. Signup and view all the answers

What is rate of change the same as?

Slope. Signup and view all the answers

What are f(x), g(x), and h(x) the same as?

Y. Signup and view all the answers

Are f(x) values part of the domain or range?

False Signup and view all the answers

If you are asked to evaluate a function given f(3), where do you put the 3?

Plug it in for x. Signup and view all the answers

If you are asked to evaluate a function given f(x)=6, where do you put the 6?

Plug it in for y. Signup and view all the answers

What type of correlation does the situation have: As one variable increases the other variable decreases?

Negative. Signup and view all the answers

What type of correlation does the situation have: As one variable increases the other variable increases?

Positive. Signup and view all the answers

What type of correlation does the situation have: Your grade and the type of hair color you have?

No correlation. Signup and view all the answers

What does the y-intercept represent in a real-world problem?

The starting point or one-time event. Signup and view all the answers

What does the slope represent in real-world problems?

The value that is occurring MULTIPLE times; Rate of Change (y per x). Signup and view all the answers

If the line on a graph is a horizontal line, what type of slope does it have?

Zero. Signup and view all the answers

If the line on a graph is a vertical line, what type of slope does it have?

Undefined. Signup and view all the answers

What letter is used to represent the correlation coefficient on the calculator?

r. Signup and view all the answers

Given $y=3-2x$, what is the slope?

-2. Signup and view all the answers

Will the axis of symmetry of a parabola be an x= or a y= equation?

x=# because it is a vertical line. Signup and view all the answers

How do you find the slope of a line from a graph?

Pick two points and count rise over run or use stat edit, stat calc 4. Signup and view all the answers

Where is the solution to a system of equations on a graph?

The point where the two lines meet/cross/touch. Signup and view all the answers

What is the equation for a line with a slope of zero?

y=#. Signup and view all the answers

What is the equation for a line with an undefined slope?

x=#. Signup and view all the answers

In a word problem, does the slope happen one time or multiple times?

False Signup and view all the answers

In a word problem, is the y-intercept the thing that happens one time or multiple times?

False Signup and view all the answers

Each, per, daily, weekly, monthly, yearly, hourly, and rate are all key words for what?

Slope. Signup and view all the answers

What is the equation for the linear parent function?

y=x. Signup and view all the answers

What is the equation for the quadratic parent function?

y=x². Signup and view all the answers

How do you solve a system of equations in standard form?

Matrix (or get y by itself and use 2nd trace 5 enter enter enter). Signup and view all the answers

How do you solve a system of equations in y= format?

Type into y= and graph; 2nd trace 5 enter enter enter. Signup and view all the answers

What are the roots of a function?

x-intercepts. Signup and view all the answers

Where are the solutions of a quadratic function?

Where the line crosses the x-axis; the x-intercepts. Signup and view all the answers

How do you find zeros, roots, x-int, solutions for a quadratic function using a table?

Look for zeros in the y column. Signup and view all the answers

How do you find the perimeter of a figure?

Add up all the sides. Signup and view all the answers

What is the problem really asking you if it says 'which of the following represents y as a function of x?'

Which one is a function. Signup and view all the answers

What inequality symbols are used for dashed lines?

< >. Signup and view all the answers

What does this symbol mean: <?

Less than. Signup and view all the answers

What does this symbol mean: >?

Greater than. Signup and view all the answers

How are the equations of parallel lines related?

They have the same slope. Signup and view all the answers

How do you tell if a list of points or a table of points are linear, quadratic, or exponential?

Plot them and identify the shapes. Signup and view all the answers

What do the graphs of quadratic functions look like (what shape)?

U (parabola). Signup and view all the answers

What does changing the m value of a line do?

Changes steepness. Signup and view all the answers

What does changing the 4 in $y=4x+5$ do to the graph?

Changes the steepness. Signup and view all the answers

What does changing the y-intercept (b) of a line do to the graph?

Shift/translate up or down. Signup and view all the answers

What does changing the 6 in $y=7x-6$ do to the graph?

Shifts/translates up or down. Signup and view all the answers

What does the b in $y=mx+b$ stand for?

Y-intercept. Signup and view all the answers

What does the m in $y=mx+b$ stand for?

Slope. Signup and view all the answers

What are the steps for getting y by itself?

Move the x, divide to get y alone. Signup and view all the answers

How do you write the range of a quadratic with a maximum?

y ≤ the highest point's y value. Signup and view all the answers

How do you write the range of a quadratic with a minimum?

y ≥ the lowest point's y value. Signup and view all the answers

What point does the axis of symmetry on a quadratic function go through?

Vertex. Signup and view all the answers

What does changing the sign of m do to a graph?

Flips direction (reflection). Signup and view all the answers

How do you find the solution to a linear inequality?

Any point in the shaded region or on a solid line. Signup and view all the answers

What do you have to do first before you can type this in to the calculator: $x²-6x=10$?

Subtract 10 from each side so all terms are on one side of the =. Signup and view all the answers

When explaining in words what slope represents, what do you say first, the x quantity or the y quantity?

List what Y stands for first. Signup and view all the answers

What does the word initial mean?

Beginning or starting point. Signup and view all the answers

What are the four vocabulary words that describe where the parabola crosses/touches the x-axis?

Zeros, Roots, X-int, Solutions. Signup and view all the answers

How will the multiple choice answers for slope questions try to trick you?

One of the answer choices will have run/rise or change in x/change in y. Signup and view all the answers

If there is a scatterplot question that is not about correlation, what do you do?

Draw a trend line. Signup and view all the answers

Where is a minimum on a parabola?

The vertex (if the parabola opens up); it's the lowest point. Signup and view all the answers

Where is the maximum of a parabola?

The vertex (if the parabola opens down); it's the highest point. Signup and view all the answers

How do you remember what rules to use when exponents are involved?

You don't have to memorize them! Use your formula chart! Signup and view all the answers

What do you do first in exponent questions?

Regular numbers, regular rules. Signup and view all the answers

Study Notes

Intercepts of Linear Equations

X-intercept of the equation y = 2x + 4 is (-2, 0).
Y-intercept of the equation is (0, 4).

Key Algebraic Concepts

A variable is represented by a letter that replaces an unknown quantity.
A constant is a standalone number in an expression without any variable.
A coefficient is the number that multiplies a variable (e.g., in 3x, the coefficient is 3).

Calculator Functions

To clear a calculator, press 2nd + 7 1 2 or 2nd + 7 all 2.
Use Math enter enter to convert a decimal to a fraction or reduce a fraction.
Parentheses are required when substituting values for variables in a calculator.

Operations in Algebra

Division denotes the quotient.
Subtraction denotes the difference.
Multiplication denotes the product.

Evaluating Expressions

When evaluating expressions with a fraction bar, solve the numerator and denominator separately before dividing.
Use the rooftop button (^) for entering exponents in the calculator.

Zero Power and Simplifying Expressions

Any non-zero number raised to the zero power equals one.
To simplify expressions, distribute and combine like terms.

Order of Operations

Follow the order: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Combining Like Terms

To combine like terms, check that the variables and their exponents are identical.
Use addition to combine coefficients of like terms.

Solving Equations and Inequalities

Goal of solving equations: isolate the variable.
Steps for solving equations: distribute, combine like terms, move constants, and isolate the variable.
For inequalities, follow similar steps but remember to flip the inequality sign when multiplying/dividing by a negative.

Graphing and Functions

Use an open bubble for < or >, and a solid bubble for ≤ or ≥ when graphing inequalities.
A function can be identified using the vertical line test.

Domain and Range

Domain: the complete set of x-values in a function.
Range: the complete set of y-values in a function.

Intercepts and Roots

X-intercepts (or zeros) occur when y = 0.
Y-intercepts always occur at x = 0.

Characteristics of Linear Functions

A linear function is represented by a straight line.
The slope is denoted by the letter 'm'.

Real World Applications

The y-intercept in real-world scenarios represents starting points, while the slope typically denotes rates of change.

Types of Correlation

Positive correlation: as one variable increases, the other does as well.
Negative correlation: as one variable increases, the other decreases.
No correlation: variables do not relate in any measurable way.

Quadratic Functions

The vertex of a parabola defines its maximum or minimum point.
The axis of symmetry for parabolas is defined by the line x = #.

Analyzing Graphs

The shape of the graph indicates the type of function: linear (straight line), quadratic (U-shaped), and exponential (curves).
Changes to the slope ('m') impact the steepness of the line, while changes to the y-intercept ('b') shift the graph up or down.

Systems of Equations

Solve by finding the point where two lines intersect.
Use matrix methods or graphing to find solutions.

Understanding Exponents

In problems involving exponents, regular numbers follow standard arithmetic rules before applying exponent rules.

Miscellaneous

The term "initial" indicates a starting point.
The correlation coefficient is represented by 'r' on calculators, conveying the strength and direction of a relationship between variables.

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Description

This quiz focuses on intercepts of linear equations, key algebraic concepts, calculator functions, and operations in algebra. Test your understanding of variables, constants, coefficients, and how to evaluate expressions effectively. Perfect for reinforcing algebra fundamentals.