Question

a line passes through the point (-6, -3) 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 \((-6,-3)\), so \(x_1=-6\), \(y_1 = - 3\). The slope \(m = 1\).

Step3: Substitute values into the formula

Substitute \(x_1=-6\), \(y_1=-3\) and \(m = 1\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-3)=1\times(x - (-6))\), which simplifies to \(y + 3=1(x + 6)\) or \(y+3=(x + 6)\) (since \(1\times(x + 6)=x + 6\)).

Answer:

\(y + 3=(x + 6)\)