Question

graph the following equations:

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

point: (\\_\\_\\_ , \\_\\_\\_ )
slope: \\_\\_\\_
(there is a coordinate grid image here)

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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. We can rewrite the given equation \(y + 4=-\frac{2}{3}(x - 2)\) in the form \(y-(- 4)=-\frac{2}{3}(x - 2)\).

Step2: Identify the point

By comparing \(y-(-4)=-\frac{2}{3}(x - 2)\) with \(y - y_1=m(x - x_1)\), we can see that \(x_1 = 2\) and \(y_1=-4\). So the point on the line is \((2,-4)\).

Step3: Identify the slope

Again, by comparing with the point - slope form \(y - y_1=m(x - x_1)\), the slope \(m =-\frac{2}{3}\).

Answer:

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