Question

Write an equation of a line in slope-intercept form with the given slope and$y$-intercept. Then graph the equation.

Slope:$-2$, $y$-intercept:$-9$

Short answer

The equation of a line in slope-intercept form with the given slope and $y$-intercept is.

$y=-2x-9$

The graph of the equation$y=-2x-9$is:

Step-by-step solution

Step 1. Write the slope-intercept form of a line.

The equation of line in slope-intercept form is:

$y=mx+b$

Where$m$ is the slope of the line and$b$ is the $y$-intercept of the line.

Step 2. Write the equation of a line in slope-intercept form having slope −2 and y-intercept −9.

The slope of the line is $-2$. Therefore, the value of$m$is $-2$.

The $y$-intercept of the line is $-9$. Therefore, the value of$b$is $-9$.

Now substitute$-2$for$m$and$-9$for$b$in the equation$y=mx+b$to find the slope-intercept form of the line.

$$\begin{gathered} y=mx+b \\ =\left(-2\right)x+\left(-9\right) \\ =-2x-9 \end{gathered}$$

Therefore, the equation of a line in slope-intercept form with the given slope and $y$-intercept is $y=-2x-9$.

Step 3. Draw the graph of the equation y=−2x−9.

The graph of the equation $y=-2x-9$is: