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?\
$y - 12 = -5(x + 2)$\
$y + 12 = -5(x - 2)$\
$y - 12 = 2(x + 2)$\
$y + 12 = 2(x - 2)$

Explanation:

Step1: Recall point - slope formula

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

Step2: Identify the slope and the point

The function is \(f(x)=- 5x + 2\). For a linear function in the form \(y = mx + b\), the slope \(m=-5\). The line contains the point \((x_1,y_1)=(-2,12)\).

Step3: Substitute into point - slope formula

Substitute \(x_1=-2\), \(y_1 = 12\) and \(m=-5\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We know that \(x_1=-2\), so \(x - x_1=x-(-2)=x + 2\), \(y_1 = 12\), so \(y - y_1=y - 12\) and \(m=-5\).
Substituting these values, we get \(y - 12=-5(x + 2)\).

Answer:

\(y - 12=-5(x + 2)\) (the first option)