Algebra Basics Unit Test Flashcards
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Questions and Answers

What is the slope-intercept form of an equation of a line?

y=mx+b

What kind of line has a slope of zero?

horizontal

What kinds of lines in a system of equations have infinitely many solutions?

2 same lines

What form of an equation of a line is Ax+By=C?

<p>Standard Form</p> Signup and view all the answers

What kinds of lines in a system of equations have no solution?

<p>2 parallel lines</p> Signup and view all the answers

What is the solution to 2 intersecting lines in a system of equations?

<p>the ordered pair where they intersect</p> Signup and view all the answers

What is the equation x=-b/2a?

<p>axis of symmetry</p> Signup and view all the answers

The equation y=6 is what kind of line?

<p>horizontal</p> Signup and view all the answers

What is the formula for finding the slope between 2 points?

<p>y-y/x-x</p> Signup and view all the answers

What are the 3 kinds of solutions a system of equations can have?

<p>no solution, infinitely many solutions, one solution</p> Signup and view all the answers

What method do you use to factor a trinomial?

<p>grouping</p> Signup and view all the answers

What are the 3 kinds of solutions a quadratic equation can have?

<p>one solution, two solutions, no real solution</p> Signup and view all the answers

The equation of a horizontal line is...

<p>y= a number</p> Signup and view all the answers

In y=mx+b, which variable is the slope?

<p>m</p> Signup and view all the answers

What is the slope when your answer is 2/0?

<p>undefined</p> Signup and view all the answers

In y=mx+b, which variable is the y-intercept?

<p>b</p> Signup and view all the answers

What is the standard form of an equation of a line?

<p>Ax+By=C</p> Signup and view all the answers

What is the equation for the axis of symmetry?

<p>-b/2a</p> Signup and view all the answers

What form of an equation of a line is y=mx+b?

<p>slope intercept form</p> Signup and view all the answers

What must the discriminant be for a polynomial to be factored?

<p>positive or perfect square</p> Signup and view all the answers

What is the expression b^2-4ac?

<p>discriminant</p> Signup and view all the answers

What is the slope of a horizontal line?

<p>zero</p> Signup and view all the answers

What kind of line has an undefined slope?

<p>vertical</p> Signup and view all the answers

What is the slope when your answer is 0/4?

<p>zero</p> Signup and view all the answers

What do you need to write an equation in point-slope form?

<p>points and slope</p> Signup and view all the answers

What is m in y=mx+b?

<p>slope</p> Signup and view all the answers

What is the quadratic formula?

<p>X=-b±√b²−4ac/(over)2a</p> Signup and view all the answers

If the discriminant is negative, how many solutions does the quadratic equation have?

<p>no real solutions</p> Signup and view all the answers

What is x^2*x^2?

<p>x^4</p> Signup and view all the answers

The equation of a vertical line is...

<p>x= a number</p> Signup and view all the answers

What form of an equation of a line is y-y=m(x-x)?

<p>point slope form</p> Signup and view all the answers

What is the solution to parallel lines in a system of equations?

<p>no solution (same line)</p> Signup and view all the answers

What does the solution to a system of equations look like?

<p>ordered pair</p> Signup and view all the answers

What are 3 ways to solve a system of equations?

<p>graphing, elimination, substitution</p> Signup and view all the answers

The discriminant is...

<p>b^2-4ac</p> Signup and view all the answers

The slopes of perpendicular lines are...

<p>negative reciprocals</p> Signup and view all the answers

What do you need to write an equation in slope-intercept form?

<p>slope (m) and intercept (b)</p> Signup and view all the answers

What is b in y=mx+b?

<p>y-intercept</p> Signup and view all the answers

What is x^2+x^2?

<p>2x^2</p> Signup and view all the answers

If the discriminant is positive, how many solutions does the quadratic equation have?

<p>2 real solutions</p> Signup and view all the answers

The equation x=-4 is what kind of line?

<p>vertical</p> Signup and view all the answers

What does the answer look like when you factor a trinomial?

<p>2 binomials in parentheses</p> Signup and view all the answers

What can you use to find the slope between two points on a graph?

<p>rise over run</p> Signup and view all the answers

What are 4 ways to solve a quadratic equation?

<p>quadratic formula, completing the square, factoring, graphing</p> Signup and view all the answers

What is the slope of a vertical line?

<p>undefined</p> Signup and view all the answers

The slopes of parallel lines are...

<p>the same</p> Signup and view all the answers

Study Notes

Slope and Equation Forms

  • Slope-intercept form is expressed as y = mx + b where m is the slope and b is the y-intercept.
  • The standard form of an equation of a line is Ax + By = C.
  • The point-slope form is represented as y - y1 = m(x - x1).

Types of Lines

  • A horizontal line has a slope of zero and can be represented as y = a number.
  • A vertical line has an undefined slope and can be represented as x = a number.

Solutions in Systems of Equations

  • Two identical (same) lines yield infinitely many solutions.
  • Parallel lines have no solution as they never intersect.
  • The solution for intersecting lines is the ordered pair where they meet.

Quadratic Equations

  • The quadratic formula is x = -b ± √(b² - 4ac) / 2a.
  • The discriminant (b² - 4ac) determines the nature of solutions in a quadratic equation:
    • Positive: Two real solutions.
    • Zero: One real solution.
    • Negative: No real solutions.

Slope Basics

  • The formula for finding slope between two points is (y₂ - y₁) / (x₂ - x₁), also known as rise over run.
  • The slopes of perpendicular lines are negative reciprocals of each other.
  • A slope of 2/0 is undefined, while a slope of 0/4 is zero.

Factoring and Solutions

  • To factor a trinomial, use the grouping method, resulting in 2 binomials in parentheses.
  • Common methods for solving systems of equations include graphing, elimination, and substitution.

Important Variables

  • In the equation y = mx + b:
    • m denotes the slope.
    • b denotes the y-intercept.

Miscellaneous Facts

  • A line with an equation y = 6 is horizontally aligned.
  • The axis of symmetry for quadratic equations is given by x = -b / 2a.

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Test your understanding of algebraic concepts with these flashcards focused on slope-intercept form, types of lines, and equations of lines. This quiz is ideal for beginners and those looking to reinforce their algebra skills. Get ready to sharpen your knowledge in foundational algebra!

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