Question

the slope - intercept form of the equation of a line that passes through point (-2, -13) is y = 5x - 3. what is the point - slope form of the equation for this line?
○ y - 13 = 5(x - 2)
○ y + 13 = 5(x + 2)
○ y - 2 = 5(x - 13)
○ y + 2 = 5(x + 13)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line 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.

First, we need to find the slope of the line from the slope - intercept form \(y = 5x-3\). In the slope - intercept form \(y=mx + b\), the slope \(m = 5\).

We are given a point \((x_1,y_1)=(- 2,-13)\) that the line passes through.

Step2: Substitute into point - slope formula

Substitute \(m = 5\), \(x_1=-2\) and \(y_1 = - 13\) into the point - slope formula \(y - y_1=m(x - x_1)\).

We get \(y-(-13)=5(x - (-2))\), which simplifies to \(y + 13=5(x + 2)\).

Answer:

\(y + 13=5(x + 2)\) (corresponding to the option \(y + 13 = 5(x + 2)\))