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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

 

CLICK HERE FOR SOLUTION 

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.

GONDOLA RIDE

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

 

CLICK HERE FOR SOLUTION

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?

blank_grid.png

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Example Four

Samuel graphed the equation shown below.

 A_3_9_Sample_4_eq.png

What is the y-intercept of the line?

blank_grid.png

CLICK HERE FOR SOLUTION

Additional Examples

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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