Question

a line passes through the point $(-8, -9)$ and has a slope of $-1$. 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 \((-8,-9)\), so \(x_1=-8\) and \(y_1 = - 9\). The slope \(m=-1\).

Step3: Substitute values into the formula

Substitute \(x_1=-8\), \(y_1=-9\) and \(m = - 1\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-9)=-1(x - (-8))\), which simplifies to \(y + 9=-1(x + 8)\).

Answer:

\(y + 9=-1(x + 8)\)