Question

the point r(7,4) is contained in line m that is parallel to the line y = 3x. which of the following equations best represents line m?
a 7x + 4y = 3
b y = 3x+7
c y = 3x
d y - 4 = 3(x - 7)

Explanation:

Step1: Find the slope of the given line

The line $y = 3x$ is in slope - intercept form $y=mx + b$ where $m$ is the slope. So the slope of $y = 3x$ is $m = 3$. Parallel lines have the same slope.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. We have the point $R(7,4)$ and $m = 3$. Substituting $x_1 = 7$, $y_1=4$ and $m = 3$ into the point - slope form, we get $y - 4=3(x - 7)$.

Answer:

D. $y - 4=3(x - 7)$