Algebra 1 Slopes Flashcards

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Questions and Answers

What is the slope formula?

  • Y1 - Y2 / X1 - X2
  • Y1 + Y2 / X1 - X2
  • Y2 + Y1 / X2 + X1
  • Y2 - Y1 / X2 - X1 (correct)

What is the slope-intercept formula?

y = mx + b

What is the standard formula for a linear equation?

Ax + By = C

What are the steps for graphing linear equations?

<ol> <li>Write the equation in slope-intercept form. 2. Graph the y-intercept at (0, b). 3. Use the slope to create more points. 4. Draw a line through the points with arrows on both ends.</li> </ol> Signup and view all the answers

What are the 4 types of slopes?

<p>Positive, Negative, Zero, Undefined (D)</p> Signup and view all the answers

What is the rise in a linear equation?

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

What is the run in a linear equation?

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

If the slope is 2 and the y-intercept is (0, -1), what is it in slope-intercept form?

<p>y = 2x - 1</p> Signup and view all the answers

When graphing a point, where should you put the point?

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

What is the slope of the equation '3x - 2y = -14'?

<p>3/2</p> Signup and view all the answers

What is the y-intercept of the equation '3x - 2y = -14'?

<p>(0, 7)</p> Signup and view all the answers

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Study Notes

Slope Concepts in Algebra 1

  • Slope Formula: Represents the rate of change; calculated using Y2-Y1/X2-X1.
  • Slope-Intercept Formula: Used for linear equations; formatted as y=mx+b, where m is the slope and b is the y-intercept.
  • Standard Form of Linear Equations: A common way to express linear equations, given as Ax + By = C, where A, B, and C are constants.

Graphing Linear Equations

  • To graph linear equations, first convert to slope-intercept form.
  • Start by plotting the y-intercept at the point (0,b).
  • Use the slope to determine additional points, employing the rise/run method.
  • Draw a line through the points using a ruler, adding arrows at both ends to indicate continuation.

Types of Slopes

  • Positive Slope: Indicates that as x increases, y also increases.
  • Negative Slope: Indicates that as x increases, y decreases.
  • Zero Slope: Represented by a horizontal line, indicating no change in y as x varies.
  • Undefined Slope: Associated with vertical lines, where x remains constant regardless of y.

Key Definitions

  • Rise: Refers to the vertical change between two points on a graph.
  • Run: Stands for the horizontal change between two points on a graph.
  • Y-intercept for the equation "3x - 2y = -14" is found at (0, 7) after rearranging into slope-intercept form.

Slope-Intercept Form Example

  • Given a slope of 2 and a y-intercept of (0, -1), the equation translates to y = 2x - 1.

Point Placement When Graphing

  • When graphing a point, begin by placing it at the y-intercept.

Slope Calculation Example

  • For the equation "3x - 2y = -14", the slope, after manipulation, is calculated as 3/2.

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