Question

mr. shaw graphs the function f(x) = -5x + 2 for his class. the line contains the point (-2, 12). what is the point - slope form of the equation of the line he graphed?
\\(\circ\\) \\(y - 12 = -5(x + 2)\\)
\\(\circ\\) \\(y - 12 = 2(x + 2)\\)
\\(\circ\\) \\(y + 12 = 2(x - 2)\\)
\\(\circ\\) \\(y + 12 = -5(x - 2)\\)

Explanation:

Step1: Recall Point - Slope Form

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

First, we need to find the slope of the line $f(x)=- 5x + 2$. For a linear function in the form $y = mx + b$, the slope $m$ is the coefficient of $x$. So, for $f(x)=-5x + 2$, the slope $m=-5$.

Step2: Identify the Point

We are given that the line passes through the point $(-2,12)$. So, $x_1=-2$ and $y_1 = 12$.

Step3: Substitute into Point - Slope Form

Substitute $m=-5$, $x_1=-2$, and $y_1 = 12$ into the point - slope form $y - y_1=m(x - x_1)$.

We know that $x - x_1=x-(-2)=x + 2$ and $y - y_1=y - 12$. And $m=-5$.

So, the equation becomes $y - 12=-5(x + 2)$.

Answer:

$y - 12=-5(x + 2)$ (corresponding to the first option: $y - 12=-5(x + 2)$)