Question

graph this line using the slope and y-intercept:
y = 7x - 8
click to select points on the graph.

Explanation:

Step1: Identify slope and y-intercept

The equation \( y = 7x - 8 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 7=\frac{7}{1} \) and \( b=- 8 \). So the y - intercept is at the point \( (0,-8) \).

Step2: Plot the y - intercept

On the coordinate plane, find the point where \( x = 0 \) and \( y=-8 \). Mark this point.

Step3: Use the slope to find another point

The slope \( m=\frac{7}{1} \) means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), there is a rise of \( 7 \) (increase in \( y \) by \( 7 \)). Starting from the y - intercept \( (0,-8) \), if we move \( 1 \) unit to the right (increase \( x \) by \( 1 \) to \( x = 1 \)) and \( 7 \) units up (increase \( y \) by \( 7 \) to \( y=-8 + 7=-1 \)), we get the point \( (1,-1) \). We can also move in the opposite direction: from \( (0,-8) \), move \( 1 \) unit to the left ( \( x=- 1 \)) and \( 7 \) units down ( \( y=-8-7=-15 \)), but \( (1,-1) \) is easier to plot on the given grid.

Step4: Draw the line

Draw a straight line passing through the points \( (0,-8) \) and \( (1,-1) \) (and other points found using the slope if needed) to represent the line \( y = 7x-8 \).

Answer:

To graph \( y = 7x - 8 \):

1. Plot the y - intercept at \( (0,-8) \).
2. Use the slope \( 7\) (rise \( 7\), run \( 1\)) to find another point, e.g., from \( (0,-8) \), move right \( 1\), up \( 7\) to get \( (1,-1) \).
3. Draw a line through these points.