Write Linear Functions from a Graph: Mini-Lesson Review

Mini Lesson Question

Question #1: Write Linear Functions from a Graph

Which function could represent the graph?

$f(x)=-2 x+2$
$f(x)=2 x+4$
$f(x)=-\frac{1}{2}x +4$
$f(x)=-2x+4$

Write Linear Functions from a Graph

You can determine the slope and intercept of a line if the equation is written in slope-intercept form, $y = m x + b$ . You can also do the reverse—identify the slope and $y$ -intercept and use them to find the equation of the line.

Write the linear function shown in the graph.

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. A line intercepts the y-axis at (0, negative 4), passes through the plotted point (3, negative 2), and intercepts the x-axis at (4, 0).

To find the slope, choose two points on the graph. The $y$ -intercept is $(0, - 4)$ , and the graph passes through $(3, - 2)$ .

Step 1 - Find the slope by counting the rise and run.

$m = \frac{r i s e}{r u n}$

Step 2 - $m = \frac{2}{3}$

Step 3 - Find the $y$ -intercept.

$y$ -intercept $(0, - 4)$

Step 4 - Substitute the values into $y = m x + b$ .

$y = m x + b$

Step 5 - $y = \frac{2}{3} x = 4$

Step 6 - Rewrite the equation using function notation.

$f (x) = \frac{2}{3} x - 4$

Try it

Write Linear Functions from a Graph

Write the linear function shown in the graph.

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted. A line intercepts the y-axis at (0, 3), and passes through the point (3, negative 1).

Here is how to write a linear function from a graph.

Step 1 - Choose two points from the graph.

$(0, 3)$ and $(3, - 1)$

Step 2 - Find the slope by counting the rise and run.

$m = \frac{r i s e}{r u n}$

Step 3 - $m = - \frac{4}{3}$

Step 4 - Find the $y$ -intercept.

$(0, 3)$

Step 5 - Substitute the values into $y = m x + b$ .

$y = m x + b$

Step 6 -

$y = - \frac{4}{3} x + 3$

Step 7 - Rewrite the equation using function notation.

$f (x) = - \frac{4}{3} x + 3$

Check Your Understanding

Which linear function could represent the graph?

The graph shows the x y-coordinate plane. The x and y-axes each run from negative 6 to 6. A line intercepts the y-axis at (0, 1) and passes through the plotted point (5, 4).

$f (x) = \frac{3}{5} x + 1$
$f (x) = \frac{5}{3} x + 1$
$f (x) = - \frac{3}{5} x + 1$
$f (x) = \frac{3}{5} x - \frac{5}{3}$

$f (x) = \frac{3}{5} x + 1$

Check yourself: The $y$ -intercept is $(0, 1)$ . Use the points $(5, 4)$ and $(0, 1)$ to find the slope, $\frac{3}{5}$ .

Video: Write Linear Equations from a Graph

Watch the following video to learn more about writing linear functions from a graph..

Khan Academy: Write Linear Equations

Access multimedia content