Question

write an equation in point - slope form for the line that passes through the point with the given slope. (-2, 1), $m = \frac{4}{3}$

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is \(y - y_1=m(x - x_1)\), 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 the point \((-2,11)\), so \(x_1=-2\) and \(y_1 = 11\). The slope \(m=\frac{4}{3}\).

Step3: Substitute values into the formula

Substitute \(x_1=-2\), \(y_1 = 11\) and \(m=\frac{4}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 11=\frac{4}{3}(x-(-2))\), which simplifies to \(y - 11=\frac{4}{3}(x + 2)\).

Answer:

\(y - 11=\frac{4}{3}(x + 2)\)