Question

the points (4, 1) and (x, -6) lie on the same line. if the slope of the line is 1, what is the value of x?
○ x = -3
○ x = 3
○ x = 9
○ x = 11

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 $(x_1,y_1)=(4,1)$, $(x_2,y_2)=(x,-6)$, and $m=1$.
$$1=\frac{-6-1}{x-4}$$

Step3: Simplify numerator

$$1=\frac{-7}{x-4}$$

Step4: Solve for $x$

Multiply both sides by $x-4$: $x-4=-7$
Add 4 to both sides: $x=-7+4=-3$

Answer:

A. $x = -3$