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MA.912.A.3.9 Slope and Intercepts

What You Need To Know...

Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on a line.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Respons).
  2. Equations of lines may be represented in various forms including slope-intercept, standard, and point-slope.
  3. Items may include lines with zero slope or undefined slope.
  4. Items may be in real-world or mathematical context.

Example One

An architect designed an outdoor staircase for a house.  The relationship between the height of the steps and the length of the tread is modeled by the equation 57x   95y = 0.

Which of the following represents the slope of the equation?

A3-9 Answers.jpg



Example Two

An engineer needs to determine the slope between two points on a gondola ride in order to evaluate the power requirements when the gondola is full of passengers.  A coordinate grid has been placed over a diagram between the two points, as shown below.  For estimation purposes, a straight line between the two points can be used to find the slope.


3-9B Image.jpg


Assuming the cable runs in a straight line, what is the slope of the line between the two points shown?

Answer grid.jpg



Example Three

Brianna plotted the two points (20, 75) and (45, 150) on a graph.  What is the x-coordinate of the x-intercept of the line that contains these two points?



Example Four

Samuel graphed the equation shown below.


What is the y-intercept of the line?



Additional Examples



Finding Intercepts

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Slope from Graphs

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Slope from Points

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Horizontal & Vertical Lines

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Reference Sheet