Question

a line has a slope of -1/4 and includes the points (7, p) and (-5, -1). what is the value of p?

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $m =-\frac{1}{4}$, $(x_1,y_1)=(7,p)$ and $(x_2,y_2)=(-5,-1)$.

Step2: Substitute values into formula

$-\frac{1}{4}=\frac{-1 - p}{-5 - 7}$.

Step3: Simplify the denominator

The denominator $-5 - 7=-12$. So, $-\frac{1}{4}=\frac{-1 - p}{-12}$.

Step4: Cross - multiply

Cross - multiplying gives $-1\times(-12)=4\times(-1 - p)$.

Step5: Expand the right - hand side

$12=-4-4p$.

Step6: Solve for $p$

Add 4 to both sides: $12 + 4=-4p$, so $16=-4p$. Then divide both sides by - 4, we get $p=-4$.

Answer:

$p = - 4$