Question

write an equation of the line that passes through ($\frac{9}{5}$, - 2) with a slope of - 5
$y=-5x+square$

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 $m=-5$, so the equation is $y=-5x + b$.

Step2: Substitute the point into the equation

Substitute the point $(\frac{9}{5},-2)$ into $y=-5x + b$. We get $-2=-5\times\frac{9}{5}+b$.

Step3: Solve for $b$

First, simplify the right - hand side of the equation: $-5\times\frac{9}{5}=-9$. So the equation becomes $-2=-9 + b$. Add 9 to both sides: $b=-2 + 9=7$.

Answer:

$y=-5x + 7$