Question

the points (7, 7) and (s, 8) fall on a line with a slope of -1/4. what is the value of s?

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(7,7)$ and $(x_2,y_2)=(s,8)$, and $m =-\frac{1}{4}$.

Step2: Substitute values into slope - formula

Substitute the values into the formula: $-\frac{1}{4}=\frac{8 - 7}{s - 7}$.

Step3: Cross - multiply

Cross - multiplying gives $-(s - 7)=4\times(8 - 7)$.

Step4: Simplify the equation

Simplify the right - hand side: $-(s - 7)=4$. Then, distribute the negative sign on the left - hand side: $-s + 7=4$.

Step5: Solve for s

Subtract 7 from both sides: $-s=4 - 7=-3$. Multiply both sides by - 1 to get $s = 3$.

Answer:

3