Question

which equation represents a line that passes through (-9, -3) and has a slope of -6?
○ y - 9 = -6(x - 3)
○ y + 9 = -6(x + 3)
○ y - 3 = -6(x - 9)
○ y + 3 = -6(x + 9)

Explanation:

Step1: Recall point - slope form

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 \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((-9,-3)\), so \(x_1=-9\) and \(y_1 = - 3\). The slope \(m=-6\).

Step3: Substitute into point - slope form

Substitute \(x_1=-9\), \(y_1=-3\) and \(m = - 6\) into the point - slope form \(y - y_1=m(x - x_1)\).
We get \(y-(-3)=-6(x - (-9))\), which simplifies to \(y + 3=-6(x + 9)\).

Answer:

D. \(y + 3=-6(x + 9)\)