Question

a line passes through the point $(-6, -8)$ and has a slope of $\frac{3}{2}$. write an equation in point - slope form for this line.

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.

Step2: Identify values of \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((-6,-8)\), so \(x_1=-6\) and \(y_1 = - 8\). The slope \(m=\frac{3}{2}\).

Step3: Substitute values into the formula

Substitute \(x_1=-6\), \(y_1=-8\) and \(m = \frac{3}{2}\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y-(-8)=\frac{3}{2}(x - (-6))\), which simplifies to \(y + 8=\frac{3}{2}(x + 6)\).

Answer:

\(y + 8=\frac{3}{2}(x + 6)\)