Question

a line with a slope of 3 passes through the points (9, 5) and (4, y). what is the value of y?

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line and $m$ is the slope.
Given $m =-\frac{2}{3}$, $(x_1,y_1)=(9,5)$ and $(x_2,y_2)=(4,q)$.

Step2: Substitute values into formula

Substitute into the slope - formula: $-\frac{2}{3}=\frac{q - 5}{4 - 9}$.

Step3: Simplify the denominator

$4−9=-5$, so the equation becomes $-\frac{2}{3}=\frac{q - 5}{-5}$.

Step4: Cross - multiply

Cross - multiplying gives $-2\times(-5)=3\times(q - 5)$.

Step5: Expand and solve for q

First, $-2\times(-5) = 10$, so $10 = 3q-15$.
Add 15 to both sides: $10 + 15=3q$, i.e., $25 = 3q$.
Then divide both sides by 3: $q=\frac{25}{3}$.

Answer:

$q=\frac{25}{3}$