Question

The equation of this line is y = 7x + 3. What would happen to the graph if the equation was changed to y = 2x + 6?

Answer 1

Answer:

From the graph,

• The line y = 7x + 3 is represented by a red line with y-intercept (0, 3)

• The line y = 2x + 6 is represented by a blue line with y-intercept (0, 6)

it is clear that the slope and y-intercept  have been changed.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the equation of a line

y = 7x + 3

comparing with a slope-intercept form of the line equation

y = mx+b

Here,

The slope = m = 7

y-intercept  = b = 3

Now, the equation changed to y = 2x + 6

y = 2x + 6

comparing with a slope-intercept form of the line equation

y = mx+b

Here,

The slope = m = 2

y-intercept  = b = 6

Thus, if the equation was changed to y = 2x + 6, the slope and y-intercept also get changed from m = 7 to m = 2 and b = 3 to b = 6 respectively.

The lines of both equations is also attached.

From the graph,

• The line y = 7x + 3 is represented by a red line with y-intercept (0, 3)

• The line y = 2x + 6 is represented by a blue line with y-intercept (0, 6)

it is clear that the slope and y-intercept  have been changed.