Q13. - 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: $-\frac{5}{8}$, $y$-intercept: $-2$

Step-by-Step Solution

Answer

The equation of a line in slope-intercept form with the given slope and $y$-intercept is $y=-\frac{5}{8}x-2$.

The graph of the equation $y=-\frac{5}{8}x-2$ 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 − 5 8 and y -intercept − 2 .

The slope of the line is $-\frac{5}{8}$. Therefore, the value of $m$ is $-\frac{5}{8}$.

 

The $y$-intercept of the line is $-2$. Therefore, the value of $b$ is $-2$.

 

Now substitute $-\frac{5}{8}$ for $m$ and $-2$ for $b$ in the equation $y=mx+b$ to find the slope-intercept form of the line.

$$\begin{gathered} y=mx+b \\ =\left(-\frac{5}{8}\right)x+\left(-2\right) \\ =-\frac{5}{8}x-2 \end{gathered}$$

Therefore, the equation of a line in slope-intercept form with the given slope and $y$-intercept is $y=-\frac{5}{8}x-2$.

Step 3. Draw the graph of the equation y = − 5 8 x − 2 .

The graph of the equation $y=-\frac{5}{8}x-2$ is: