Question

graph the equation.
$y - 2 = -4(x - 2)$
use the graphing tool to graph the equation.
click to enlarge graph

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 2=-4(x - 2) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(2,2) \) and the slope \( m=-4 \).

Step2: Plot the point

First, we plot the point \( (2,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = - 4=\frac{-4}{1} \). From the point \( (2,2) \), we move down 4 units (because the numerator of the slope is - 4, which represents a change in \( y \)) and then move 1 unit to the right (because the denominator of the slope is 1, which represents a change in \( x \)). So we get the point \( (2 + 1,2-4)=(3,-2) \). We can also move up 4 units and left 1 unit from \( (2,2) \) to get the point \( (2-1,2 + 4)=(1,6) \).

Step4: Draw the line

After plotting two (or more) points, we draw a straight line passing through these points. The line should have a slope of - 4 and pass through the point \( (2,2) \).

Answer:

To graph the equation \( y - 2=-4(x - 2) \):

1. Plot the point \( (2,2) \).
2. Use the slope \( m=-4 \) to find additional points (e.g., \( (3,-2) \) or \( (1,6) \)).
3. Draw a straight line through the plotted points. The line has a slope of - 4 and passes through \( (2,2) \).