Question

question 19 of 25
what is the point - slope equation of a line with slope - 4 that contains the point
(-2, 7)?
a. $y + 7=-4(x + 2)$
b. $y - 7=-4(x + 2)$
c. $y + 7=-4(x - 2)$
d. $y - 7=-4(x - 2)$

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope of the line and $(x_1,y_1)$ is a point on the line.

Step2: Identify values of $m$, $x_1$ and $y_1$

We are given that the slope $m=- 4$ and the point on the line is $(-2,7)$. So, $x_1=-2$ and $y_1 = 7$.

Step3: Substitute values into the formula

Substitute $m=-4$, $x_1=-2$ and $y_1 = 7$ into the point - slope formula $y - y_1=m(x - x_1)$.
We get $y - 7=-4(x-(-2))$.
Simplify the expression inside the parentheses: $x-(-2)=x + 2$.
So the equation becomes $y - 7=-4(x + 2)$.

Answer:

B. $y - 7=-4(x + 2)$