Question

a line has a slope of - 7 and includes the points (-6, -1) and (-7, 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, $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Here $m=-7$, $x_1=-6$, $y_1 = - 1$, $x_2=-7$, and $y_2 = j$.

Step2: Substitute values into formula

Substitute the values into the slope - formula: $-7=\frac{j-(-1)}{-7 - (-6)}$.

Step3: Simplify the denominator

Simplify the denominator: $-7-(-6)=-7 + 6=-1$. So the equation becomes $-7=\frac{j + 1}{-1}$.

Step4: Solve for $j$

Multiply both sides of the equation by $-1$: $(-7)\times(-1)=j + 1$. Then $7=j + 1$. Subtract 1 from both sides: $j=7 - 1$.

Answer:

$j = 6$