Graphing Linear Equations Worksheet

26 printable practice problems: graph lines in slope-intercept, standard and point-slope form, graph horizontal and vertical lines, and write the equation of a line from its graph. Full answer key with graphs.

26 problems · answer key included · free, no sign-up

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Teachers and parents: print the student copy for class or homework, or print with the answer key on a separate page. You can also link to this page from your course site or LMS; no account is needed. Problems get harder within each section.

A. Slope-intercept form

Identify the slope and y-intercept, plot the y-intercept, use the slope to plot a second point, then draw the line.

1
$y = 2 x + 1$
2
$y = - 3 x + 4$
3
$y = \frac{1}{2} x - 3$
4
$y = - \frac{2}{3} x + 2$
5
$y = x - 5$
6
$y = - x$
7
$y = \frac{3}{4} x + 1$
8
$y = - \frac{5}{2} x - 1$

B. Standard form (use the intercepts)

Find the x-intercept (set y = 0) and the y-intercept (set x = 0), plot both, then draw the line.

9
$2 x + 3 y = 6$
10
$x - 2 y = 4$
11
$4 x + y = - 8$
12
$3 x - 5 y = 15$
13
$- 2 x + 4 y = 8$
14
$5 x + 2 y = 10$

C. Point-slope form

Plot the point given in the equation, use the slope to find another point, and draw the line. Then write it in slope-intercept form.

15
$y - 1 = 2 (x - 3)$
16
$y + 2 = - \frac{1}{3} (x - 6)$
17
$y - 4 = - (x + 2)$
18
$y + 3 = \frac{3}{2} (x + 4)$

D. Horizontal and vertical lines

Graph each line. State its slope.

19
$y = 4$
20
$x = - 3$
21
$y = - 6$
22
$x = 5$

E. Write the equation from the graph

Use the two marked points to find the slope and y-intercept. Write the equation in slope-intercept form.

Answer key

Check your work after you finish each section.

A. Slope-intercept form

1.
$y = 2 x + 1$
$m = 2$
$y-int (0, 1)$
$x-int (- \frac{1}{2}, 0)$
Points: (0, 1), (1, 3)
2.
$y = - 3 x + 4$
$m = - 3$
$y-int (0, 4)$
$x-int (\frac{4}{3}, 0)$
Points: (0, 4), (1, 1)
3.
$y = \frac{1}{2} x - 3$
$m = \frac{1}{2}$
$y-int (0, - 3)$
$x-int (6, 0)$
Points: (0, -3), (2, -2)
4.
$y = - \frac{2}{3} x + 2$
$m = - \frac{2}{3}$
$y-int (0, 2)$
$x-int (3, 0)$
Points: (0, 2), (3, 0)
5.
$y = x - 5$
$m = 1$
$y-int (0, - 5)$
$x-int (5, 0)$
Points: (0, -5), (1, -4)
6.
$y = - x$
$m = - 1$
$y-int (0, 0)$
$x-int (0, 0)$
Points: (0, 0), (1, -1)
7.
$y = \frac{3}{4} x + 1$
$m = \frac{3}{4}$
$y-int (0, 1)$
$x-int (- \frac{4}{3}, 0)$
Points: (0, 1), (4, 4)
8.
$y = - \frac{5}{2} x - 1$
$m = - \frac{5}{2}$
$y-int (0, - 1)$
$x-int (- \frac{2}{5}, 0)$
Points: (0, -1), (2, -6)

B. Standard form (use the intercepts)

9.
$y = - \frac{2}{3} x + 2$
$m = - \frac{2}{3}$
$y-int (0, 2)$
$x-int (3, 0)$
Points: (3, 0), (0, 2)
10.
$y = \frac{1}{2} x - 2$
$m = \frac{1}{2}$
$y-int (0, - 2)$
$x-int (4, 0)$
Points: (4, 0), (0, -2)
11.
$y = - 4 x - 8$
$m = - 4$
$y-int (0, - 8)$
$x-int (- 2, 0)$
Points: (-2, 0), (0, -8)
12.
$y = \frac{3}{5} x - 3$
$m = \frac{3}{5}$
$y-int (0, - 3)$
$x-int (5, 0)$
Points: (5, 0), (0, -3)
13.
$y = \frac{1}{2} x + 2$
$m = \frac{1}{2}$
$y-int (0, 2)$
$x-int (- 4, 0)$
Points: (-4, 0), (0, 2)
14.
$y = - \frac{5}{2} x + 5$
$m = - \frac{5}{2}$
$y-int (0, 5)$
$x-int (2, 0)$
Points: (2, 0), (0, 5)

C. Point-slope form

15.
$y = 2 x - 5$
$m = 2$
$y-int (0, - 5)$
$x-int (\frac{5}{2}, 0)$
Points: (0, -5), (1, -3)
16.
$y = - \frac{1}{3} x$
$m = - \frac{1}{3}$
$y-int (0, 0)$
$x-int (0, 0)$
Points: (0, 0), (3, -1)
17.
$y = - x + 2$
$m = - 1$
$y-int (0, 2)$
$x-int (2, 0)$
Points: (0, 2), (1, 1)
18.
$y = \frac{3}{2} x + 3$
$m = \frac{3}{2}$
$y-int (0, 3)$
$x-int (- 2, 0)$
Points: (0, 3), (2, 6)

D. Horizontal and vertical lines

19.
$y = 4$
$m = 0 (horizontal)$
$y-int (0, 4)$
Points: (-3, 4), (4, 4)
20.
$x = - 3$
$undefined slope (vertical)$
$x-int (- 3, 0)$
Points: (-3, -2), (-3, 3)
21.
$y = - 6$
$m = 0 (horizontal)$
$y-int (0, - 6)$
Points: (-3, -6), (4, -6)
22.
$x = 5$
$undefined slope (vertical)$
$x-int (5, 0)$
Points: (5, -2), (5, 3)

E. Write the equation from the graph

23.
$y = 2 x - 2$
$m = \frac{4 - ( - 2 )}{3 - 0} = 2$
$b = - 2$
24.
$y = - \frac{3}{4} x + 5$
$m = \frac{2 - 5}{4 - 0} = - \frac{3}{4}$
$b = 5$
25.
$y = 3 x + 6$
$m = \frac{6 - 0}{0 - ( - 2 )} = 3$
$b = 6$
26.
$y = \frac{1}{2} x$
$m = \frac{3 - 1}{6 - 2} = \frac{1}{2}$
$b = 0$

How to graph a linear equation

1. Get it into slope-intercept form. Solve for $y$ so the equation looks like $y = m x + b$ . The number in front of $x$ is the slope $m$ , and $b$ is where the line crosses the y-axis.

2. Plot the y-intercept. Put a point at $(0, b)$ .

3. Use the slope as rise over run. For $m = \frac{3}{4}$ , move up 3 and right 4 from the y-intercept and plot a second point. For a negative slope, move down instead of up.

4. Draw the line through both points with a ruler and extend it to the edges of the grid. Check a third point: it should satisfy the original equation.

Standard form shortcut: for $A x + B y = C$ , the intercepts are $(\frac{C}{A}, 0)$ and $(0, \frac{C}{B})$ . Plot those two points and connect them.

Read the full Graphing Linear Equations lesson with worked examples →

Frequently asked questions

How do you graph a linear equation?

Write the equation in slope-intercept form, y = mx + b. Plot the y-intercept (0, b), then use the slope m as rise over run to find a second point. For a slope of 2/3, move up 2 and right 3. Draw a straight line through the two points and extend it across the grid.

What is the fastest way to graph an equation in standard form?

Use the intercepts. Set y = 0 and solve for x to get the x-intercept, then set x = 0 and solve for y to get the y-intercept. Plot both points and draw the line. For 2x + 3y = 6 the intercepts are (3, 0) and (0, 2).

How do you graph a negative slope?

A negative slope means the line falls from left to right. For a slope of -3/4, start at the y-intercept, move down 3 and right 4. Moving up 3 and left 4 gives a point on the same line.

What is the slope of a horizontal or vertical line?

A horizontal line such as y = 4 has a slope of 0. A vertical line such as x = -3 has an undefined slope, because the run is zero and you cannot divide by zero.

Is there an answer key?

Yes. Every problem has an answer with the slope, intercepts, two points on the line and a small graph to compare with. Print the student copy without answers, or print with the answer key on a separate page.

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