Question

a line with a slope of $-\frac{1}{9}$ passes through the points (5, 0) and (-4, j). what is the value of j?
j = \boxed{}

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute known values

Let $(x_1,y_1)=(5,0)$, $(x_2,y_2)=(-4,j)$, and $m=-\frac{1}{9}$.
$$-\frac{1}{9}=\frac{j-0}{-4-5}$$

Step3: Simplify denominator

Calculate $-4-5=-9$.
$$-\frac{1}{9}=\frac{j}{-9}$$

Step4: Solve for $j$

Multiply both sides by $-9$.
$$j = -\frac{1}{9} \times (-9)$$

Answer:

$1$