Q11. - Algebra 1

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: $-9$

Step-by-Step Solution

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 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 = − 2 x − 9 .

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