Question

a line with a slope of -1/2 passes through the points (8, -7) and (4, j). what is the value of j?

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Here, $m =-\frac{1}{2}$, $(x_1,y_1)=(8, - 7)$ and $(x_2,y_2)=(4,j)$.

Step2: Substitute values into formula

Substitute the values into the slope - formula: $-\frac{1}{2}=\frac{j+7}{4 - 8}$.

Step3: Simplify the denominator

$4−8=-4$, so the equation becomes $-\frac{1}{2}=\frac{j + 7}{-4}$.

Step4: Cross - multiply

Cross - multiplying gives $-1\times(-4)=2\times(j + 7)$.

Step5: Expand and solve for $j$

First, expand the right - hand side: $4 = 2j+14$. Then subtract 14 from both sides: $4-14=2j$, which simplifies to $-10 = 2j$. Divide both sides by 2: $j=-5$.

Answer:

$j=-5$