Algebra II Unit 1 Test Flashcards

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Questions and Answers

What is the slope formula?

y2 - y1 / x2 - x1

A slope is considered rising if it is a positive number.

True

A slope is considered falling if it is a negative number.

True

A slope is vertical if the denominator of the slope fraction is 0.

True Signup and view all the answers

A slope is horizontal if it is 0.

True Signup and view all the answers

Two lines are considered parallel if their slopes are...

the same Signup and view all the answers

Two lines are considered perpendicular if their slopes are...

opposite reciprocals Signup and view all the answers

What steps do you need to follow to find a missing number in a pair of points?

1: Take the slope and the numbers you do have and insert it into the slope formula; 2: Solve for the half of the fraction that doesn't have the missing value; 3: Multiply that new number by your slope; 4: Set that new number equal to the other half; 5: Solve for the unknown variable. Signup and view all the answers

What is the standard form of a linear equation?

Ax + By = C Signup and view all the answers

When finding x in standard form, what should you do?

Insert 0 for y and solve accordingly. Signup and view all the answers

When finding y in standard form, what should you do?

Insert 0 for x and solve accordingly. Signup and view all the answers

What is the slope-intercept form of a linear equation?

y = mx + b Signup and view all the answers

What is the point-slope form of a linear equation?

y - y1 = m(x - x1) Signup and view all the answers

If given a coordinate that is parallel to a given slope equation, what should you do?

Take the points & the slope from the given equation, put them into point-slope, and solve. Signup and view all the answers

If given a coordinate that is perpendicular to a given slope equation, what should you do?

Take the points & the opposite of the slope from the given equation, put them into point-slope, and solve. Signup and view all the answers

When graphing inequalities, what kind of line do you draw if the sign is < or > with a line under it?

A full line. Signup and view all the answers

When graphing inequalities, what kind of line do you draw if the sign is < or >?

A dotted line. Signup and view all the answers

What are the steps to graphing an inequality?

1: Graph the line given in the inequality; 2: Choose an available test-point on either side and insert the numbers into your inequality; 3: Solve that inequality; 4: If it is correct, shade in the side the point is on. Signup and view all the answers

How do you model linear functions?

1: Read the problem and identify your time and your numeric in both situations; 2: Write them both down in the form of a coordinate; 3: Put them into slope-intercept and solve. Signup and view all the answers

Study Notes

Slope Concepts

Slope formula is defined as ((y_2 - y_1) / (x_2 - x_1)).
A rising slope has a positive value indicating the line slopes upwards from left to right.
A falling slope has a negative value indicating the line slopes downwards from left to right.
A vertical slope occurs when the denominator in the slope formula equals zero, representing a line that goes straight up and down.
A horizontal slope has a value of zero, indicating there is no change in the y-coordinate as x varies.

Line Relationships

Two lines are parallel if they have identical slopes.
Two lines are perpendicular if their slopes are opposite reciprocals, meaning one slope could be expressed as (-1/m) if the other slope is (m).

Finding Missing Coordinates

To find a missing coordinate:
- Insert known values into the slope formula.
- Solve for the side of the fraction containing the unknown.
- Multiply the known number by the slope.
- Set the product equal to the other half of the fraction and solve for the unknown.

Forms of Linear Equations

Standard form of a linear equation is represented as (Ax + By = C).
To find (x) from a standard form equation, substitute (0) for (y) and solve.
To find (y) from a standard form equation, substitute (0) for (x) and solve.

Equation Formats

Slope-intercept form is expressed as (y = mx + b), where (m) represents the slope and (b) is the y-intercept.
Point-slope form is represented as (y - y_1 = m(x - x_1)).

Parallel and Perpendicular Lines

To establish a line parallel to a given slope, use the given slope and any point in point-slope form.
To establish a line perpendicular to a given slope, use the opposite reciprocal of the slope from the given line and apply any point in point-slope form.

Graphing Inequalities

When graphing inequalities:
- Use a solid line if the inequality sign includes an equal to (≤ or ≥).
- Use a dotted line if the inequality is strict (< or >).
Steps for graphing an inequality:
- Graph the corresponding line.
- Choose a test point to substitute into the inequality.
- Solve the inequality with the chosen coordinates.
- If the result is true, shade the region of the graph corresponding to the test point.

Modeling Linear Functions

Model linear functions by identifying time and numeric conditions relevant to the scenario.
Represent these conditions as coordinates.
Use the coordinates to formulate the problem into slope-intercept form and solve accordingly.

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Description

These flashcards cover key concepts from Unit 1 of Algebra II, focusing on the slope formula and its characteristics. Learn how to identify rising, falling, and vertical slopes through definitions and explanations. Perfect for students preparing for their Algebra II assessments.