Question

graph this line:
y - 2 = 3(x + 2)
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and a submit button at the bottom left)

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 2 = 3(x + 2) \), which is in point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. Here, \( m = 3 \) and the point \( (x_1,y_1)=(- 2,2) \).

Step2: Find another point using the slope

The slope \( m = 3=\frac{3}{1} \), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), the rise is \( 3 \) (increase in \( y \) by \( 3 \)). Starting from the point \( (-2,2) \), if we add \( 1 \) to \( x \) ( \( x=-2 + 1=-1 \)) and add \( 3 \) to \( y \) ( \( y = 2+3 = 5 \)), we get the point \( (-1,5) \). We can also find the \( y \)-intercept by converting the equation to slope - intercept form (\( y=mx + b \)).
Expand the given equation:
\( y-2=3x + 6 \)
Add \( 2 \) to both sides: \( y=3x+6 + 2=3x + 8 \). So the \( y \)-intercept is \( (0,8) \).

Step3: Plot the points

First, plot the point \( (-2,2) \) (since \( x=-2,y = 2 \)). Then plot the point \( (0,8) \) (from the \( y \)-intercept) or \( (-1,5) \). After plotting two points, draw a straight line passing through them.

Answer:

To graph the line \( y - 2=3(x + 2) \):

1. Identify the point from the point - slope form: The point \( (-2,2) \) lies on the line.
2. Convert to slope - intercept form: \( y = 3x+8 \), so the \( y \)-intercept is \( (0,8) \).
3. Plot the points \( (-2,2) \) and \( (0,8) \) (or other points found using the slope) and draw a straight line through them.