Question

a line passes through the point (-5, -7) and has a slope of 4. 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 \((-5,-7)\), so \(x_1=-5\), \(y_1 = - 7\). The slope \(m = 4\).

Step3: Substitute values into the formula

Substitute \(x_1=-5\), \(y_1=-7\) and \(m = 4\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y-(-7)=4(x - (-5))\), which simplifies to \(y + 7=4(x + 5)\).

Answer:

\(y + 7=4(x + 5)\)