Question

graph these equations:
y = 4x - 1
y = 4x - 9
click to select points on the graph.

Explanation:

Step1: Analyze \( y = 4x - 1 \)

The equation is in slope - intercept form \( y=mx + b \), where \( m = 4 \) (slope) and \( b=-1 \) (y - intercept). To find a point, when \( x = 0 \), \( y=4(0)-1=-1 \), so the y - intercept is \( (0,-1) \). Using the slope (rise over run, \( \frac{4}{1} \)), from \( (0,-1) \), moving 1 unit right and 4 units up gives \( (1,3) \).

Step2: Analyze \( y = 4x - 9 \)

For the equation \( y = 4x-9 \), in slope - intercept form, \( m = 4 \) and \( b = - 9 \). When \( x = 0 \), \( y=4(0)-9=-9 \), so the y - intercept is \( (0,-9) \). Using the slope \( \frac{4}{1} \), from \( (0,-9) \), moving 1 unit right and 4 units up gives \( (1,-5) \).

To graph:

• For \( y = 4x - 1 \), plot the points \( (0,-1) \) and \( (1,3) \) (and other points using the slope) and draw a line through them.
• For \( y = 4x - 9 \), plot the points \( (0,-9) \) and \( (1,-5) \) (and other points using the slope) and draw a line through them. The two lines will be parallel since they have the same slope (\( m = 4 \)) and different y - intercepts.

Answer:

To graph \( y = 4x - 1 \): Plot \( (0,-1) \), then use slope \( 4 \) (up 4, right 1) to get more points (e.g., \( (1,3) \), \( (2,7) \) etc.) and draw the line.
To graph \( y = 4x - 9 \): Plot \( (0,-9) \), then use slope \( 4 \) (up 4, right 1) to get more points (e.g., \( (1,-5) \), \( (2,-1) \) etc.) and draw the line. The two lines are parallel.