Question

graph this line:
y - 3 = -4(x + 8)
click to select points on the graph.

Explanation:

Step1: Identify the form of the equation

The given equation \( y - 3 = -4(x + 8) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( m=-4 \) (the slope) and the point \( (x_1,y_1)=(-8,3) \) (since \( x_1=-8 \) (because \( x - (-8)=x + 8 \)) and \( y_1 = 3 \)).

Step2: Plot the point from point - slope form

First, we plot the point \( (-8,3) \) on the coordinate plane. To find another point, we can use the slope. The slope \( m=-4=\frac{-4}{1} \), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), the rise is \( - 4 \) (decrease in \( y \) by \( 4 \)).

Starting from the point \( (-8,3) \), if we add \( 1 \) to \( x \) (so \( x=-8 + 1=-7 \)) and subtract \( 4 \) from \( y \) (so \( y=3-4=-1 \)), we get the point \( (-7,-1) \).

We can also rewrite the equation in slope - intercept form (\( y=mx + b \)) to check.
Expand the right - hand side of the equation:
\( y-3=-4x-32 \)
Add \( 3 \) to both sides:
\( y=-4x-32 + 3=-4x-29 \)
When \( x = 0 \), \( y=-29 \), but \( -29 \) is not in the range of the given graph. So using the point - slope form to find points is more convenient for this graph.

To graph the line, we plot the point \( (-8,3) \) and then use the slope to find another point (like \( (-7,-1) \)) and draw a straight line through these points.

Answer:

To graph the line \( y - 3=-4(x + 8) \):

1. Plot the point \( (-8,3) \) (since the equation is in point - slope form \( y - y_1=m(x - x_1) \) with \( (x_1,y_1)=(-8,3) \) and \( m = - 4 \)).
2. Use the slope \( m=-4=\frac{\text{rise}}{\text{run}}=\frac{-4}{1} \). From the point \( (-8,3) \), move 1 unit to the right (increase \( x \) by 1) and 4 units down (decrease \( y \) by 4) to get the point \( (-7,-1) \).
3. Draw a straight line through the points \( (-8,3) \) and \( (-7,-1) \) (and extend it in both directions).