Question

a line with a slope of -1/6 passes through the points (d, 3) and (-9, 0). what is the value of d?

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, $m = \frac{1}{6}$, $(x_1,y_1)=(d,3)$ and $(x_2,y_2)=(-9,0)$.

Step2: Substitute values into formula

$\frac{1}{6}=\frac{0 - 3}{-9 - d}$.

Step3: Cross - multiply

$1\times(-9 - d)=6\times(-3)$.

Step4: Simplify equation

$-9 - d=-18$.

Step5: Solve for $d$

Add 9 to both sides: $-d=-18 + 9$, so $-d=-9$, and $d = 9$.

Answer:

$9$