Question

graph the line.
$y + 4 = 5(x - 3)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 4 = 5(x - 3) \), 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. Here, \( m = 5 \) and the point \( (x_1,y_1)=(3,-4) \).

Step2: Plot the point

Locate the point \( (3,-4) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = 5=\frac{5}{1} \), which means for a run of \( 1 \) unit (increase in \( x \) by \( 1 \)), the rise is \( 5 \) units (increase in \( y \) by \( 5 \)). Starting from \( (3,-4) \), if we move \( 1 \) unit to the right (increase \( x \) by \( 1 \) to \( x = 3+1 = 4 \)) and \( 5 \) units up (increase \( y \) by \( 5 \) to \( y=-4 + 5=1 \)), we get the point \( (4,1) \). We can also move in the opposite direction: for a run of \( - 1 \) (decrease \( x \) by \( 1 \) to \( x=3 - 1=2 \)) and a rise of \( - 5 \) (decrease \( y \) by \( 5 \) to \( y=-4-5=-9 \)) to get the point \( (2,-9) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (3,-4) \) and \( (4,1) \) or \( (3,-4) \) and \( (2,-9) \)).

Answer:

To graph the line \( y + 4 = 5(x - 3) \):

1. Recognize it is in point - slope form \( y - y_1=m(x - x_1) \) with slope \( m = 5 \) and point \( (3,-4) \).
2. Plot the point \( (3,-4) \) on the coordinate plane.
3. Use the slope \( m = 5 \) to find another point (e.g., from \( (3,-4) \), move 1 unit right and 5 units up to get \( (4,1) \)).
4. Draw a straight line through the plotted points.