Question

find the lines slope and a point on the line.
$y - 2 = -\frac{2}{3}(x + 4)$
slope:
point on the line: ( , )

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point on the line.

Step2: Identify slope and point from the given equation

Given the equation \(y - 2=-\frac{2}{3}(x + 4)\), we can rewrite \(x + 4\) as \(x-(-4)\). So comparing with the point - slope form \(y - y_1=m(x - x_1)\), we have:

• The slope \(m =-\frac{2}{3}\)
• The point \((x_1,y_1)\) is \((- 4,2)\) because \(x_1=-4\) and \(y_1 = 2\) (from \(y - 2\) and \(x-(-4)\))

Answer:

slope: \(-\frac{2}{3}\)
point on the line: \((-4,2)\)