Question

the points $(f, 7)$ and $(6, 10)$ fall on a line with a slope of $-3$. what is the value of $f$?
$f = $
work it out

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.
Here, $m=-3$, $(x_1,y_1)=(f,7)$, $(x_2,y_2)=(6,10)$.

Step2: Substitute values into formula

$-3=\frac{10-7}{6-f}$

Step3: Simplify numerator

$-3=\frac{3}{6-f}$

Step4: Solve for $6-f$

Multiply both sides by $6-f$: $-3(6-f)=3$
Divide both sides by $-3$: $6-f=\frac{3}{-3}=-1$

Step5: Solve for $f$

Rearrange: $f=6-(-1)=6+1$

Answer:

$7$