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Graphing Linear Functions and Inequalities Practice Problems

Practice Problem #1

You're helping a friend with homework. He is trying to graph 2y - 4x = 8 using the x and y intercepts. Your friend shows you the following possibilities for the x-intercept. Which of them is the correct x-intercept?

  1. −2
  2. 1
  3. 2
  4. 4

Practice Problem #2

Which of the following coordinates could be a y-intercept? Hint: Three of the choices could never be a y-intercept.

  1. (0,2)
  2. (1,1)
  3. (4,-3)
  4. (-5,0)

Practice Problem #3

Graph y = 3x + 2

First, identify the y-intercept.

The y-intercept is _____ (Fill in the blank).

Plot the y-intercept.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,2).

Next, identify the slope. Write it as a fraction.

The slope is _____ (Fill in the blank)

Use the slope to plot a point to the left and right of the y-intercept. Remember that slope is rise over run. Then draw a line through your points.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,2), two other points plotted at (1,5) and (-1,-1) with a line through the points

Practice Problem #4

Graph y = negative one halfx − 1.

First, identify the y-intercept.

The y-intercept is _____ (Fill in the blank).

Plot the y-intercept.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,-1)

Next, identify the slope.

The slope is _____ (Fill in the blank)

Use the slope to plot a point to the left and right of the y-intercept. Remember that slope is rise over run. Then draw a line through your points.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,2), two other points plotted at (-2,0) and (2,-2) with a line through the points

Practice Problem #5

Graph y ≤ −x + 1.

Will the line be dashed or solid?

Identify the y-intercept.

The y-intercept is _____ (Fill in the blank).

Plot the y-intercept.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,1)

Next, identify the slope. Write it as a fraction.

The slope is _____ (Fill in the blank)

Use the slope to plot a point to the left and right of the y-intercept. Remember that slope is rise over run. Draw a solid line through the points.

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,2), two other points plotted at (-1,2) and (0,1) with a line through the points

Next, choose a point to test for shading. We can test (0,0). Plug 0 in for x and y into the original equation.

y ≤ −x + 1

____ (Fill in the blank) ≤ −(____) (Fill in the blank) + 1

Simplify

0 ≤ ____ (Fill in the blank)

Is 0 less than or equal to 1? Yes

This means that the shading will be on the same side as the point (0,0).

Graph with an x-axis numbered from -8 to 8 and an y-axis numbered from -8 to 8. y-intercept plotted at (0,2), two other points plotted at (-1,2) and (0,1) with a line through the points. The bottom half or left of the graph is shaded.