Question

Reasoning How would the graph of y = - 3x + 2 change if - 3 were replaced by 4? How would it change if were replaced by 0? Explain.

Answer 1

Answer:

Please check the attached diagram.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the rate of change or slope

• b is the y-intercept

Analysis of y = - 3x + 2

Given the linear function

y = - 3x + 2

comparing with the slope-intercept form y = mx+b

The slope m = -3

The negative slope indicates that as the line on the line graph moves from left to right, the line falls.

In other words, the negative slope indicates that when x increases, y decrease, and vise versa.

Please check the attached graph of the function y = - 3x + 2. It is clear that when x increases, y decreases, hence the line falls when the graph of the line moves from left to right.

The red line graph represents the linear function y = - 3x + 2.

Analysis of y = 4x + 2   (When -3 is replaced by 4)

Now, when we replace -3 by 4 in the equation y = - 3x + 2, the equation becomes

y = 4x + 2

comparing with the slope-intercept form y = mx+b

The slope m = 4

The positive slope indicates that as the line on the line graph moves from left to right, the line rises.

In other words, the positive slope indicates that when x increases, y also increases, and vise versa.

Please check the attached graph of the function y = 4x + 2. It is clear that when x increases, y increases, hence the line rises when the graph of the line moves from left to right.

The blue line graph represents the linear function y = 4x + 2.

Analysis of y = 2   (When -3 is replaced by 0)

Given the equation

y = - 3x + 2

If we replace -3 by 0, the equation becomes

y = 0x + 2

y = 2

In other words, y = 2 represents a horizontal line because the horizontal line is of the form

y = k

where k is the y-intercept

here k = 2 is the y-intercept of the line y = 2.

Thus, slope zero means the value of y does not change no matter what we take or change the x-value.

The graph of line y = 2 is also attached which represents a horizontal line with slope 0 and y-intercept 2.

The green line graph represents the linear function y = 2.

Please check the graphs of all the lines.