Question

graph this line:
$y + 2 = 4(x - 3)$
click to select points on the graph.

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 2 = 4(x - 3) \), which is in the 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. By comparing, we can see that the slope \( m = 4 \) and the point \( (x_1,y_1)=(3,- 2) \) (since \( y_1=-2 \) when we rewrite \( y + 2\) as \( y-(-2) \)).

Step2: Plot the point

On the coordinate plane, find the point with \( x = 3\) and \( y=-2 \) and mark it.

Step3: Use the slope to find another point

The slope \( m = 4=\frac{4}{1} \), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)) and a rise of \( 4 \) (increase in \( y \) by \( 4 \)). Starting from the point \( (3,-2) \), if we move \( 1 \) unit to the right (increase \( x \) by \( 1 \), so \( x = 3 + 1=4 \)) and \( 4 \) units up (increase \( y \) by \( 4 \), so \( y=-2 + 4 = 2\)), we get the point \( (4,2) \). We can also move in the opposite direction: for a run of \( - 1\) (decrease \( x \) by \( 1 \), \( x=3-1 = 2\)) and a rise of \( - 4\) (decrease \( y \) by \( 4 \), \( y=-2-4=-6 \)), we get the point \( (2,-6) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (3,-2) \), \( (4,2) \), \( (2,-6) \)).

Answer:

To graph the line \( y + 2 = 4(x - 3) \), first plot the point \( (3,-2) \). Then, using the slope \( m = 4\), find another point (e.g., \( (4,2) \) or \( (2,-6) \)) and draw a straight line through these points.