Question

write an equation in slope - intercept form for a line that has a slope, $m = -\frac{4}{3}$, and passes through the point (-9,5).
$y = -\frac{4}{3}x - 9$
$y = -\frac{4}{3}x - 17$
$y = -\frac{4}{3}x - 7$
$y = -\frac{4}{3}x + 5$

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 $m=-\frac{4}{3}$, so the equation is $y =-\frac{4}{3}x + b$.

Step2: Substitute the point into the equation

Substitute $x=-9$ and $y = 5$ into $y=-\frac{4}{3}x + b$. We get $5=-\frac{4}{3}\times(-9)+b$.

Step3: Simplify the right - hand side

$-\frac{4}{3}\times(-9)=12$, so the equation becomes $5 = 12 + b$.

Step4: Solve for $b$

Subtract 12 from both sides: $b=5 - 12=-7$.

Step5: Write the final equation

The equation of the line in slope - intercept form is $y=-\frac{4}{3}x-7$.

Answer:

$y =-\frac{4}{3}x - 7$