Question

write an equation in slope - intercept form for a line that has a slope, $m=\frac{5}{2}$, and passes through the point $(8,0)$. $y = \frac{5}{2}x-20$ $y=\frac{5}{2}x + 8$ $y=\frac{5}{2}x-8$ $y=\frac{5}{2}x$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m=\frac{5}{2}$, so the equation becomes $y=\frac{5}{2}x + b$.

Step2: Substitute the point into the equation

Substitute the point $(x = 8,y = 0)$ into $y=\frac{5}{2}x + b$. We get $0=\frac{5}{2}\times8 + b$.

Step3: Solve for $b$

First, calculate $\frac{5}{2}\times8=20$. So the equation is $0 = 20 + b$. Then, subtract 20 from both sides to find $b=-20$.

Step4: Write the final equation

Substitute $b = - 20$ back into $y=\frac{5}{2}x + b$. The equation of the line is $y=\frac{5}{2}x-20$.

Answer:

$y=\frac{5}{2}x - 20$