Question

Compare the y-intercept and the rate of change of the following items

Answer 1

compare the y-intercept and the rate of change of the following items. Option (d) The rates of change are the same, but the y-intercepts are different. is correct.

for rates,

we will find the slope of I and II

slope = dy/dx = change in y/change in x

for both of them when we compare the slope, it is 0.3.

for y-intercepts.

equation for II should be formed in order to compare with the y-intercept of I which is 3.4.

y-7=0.3(x-12) .................(i)

so, the y-intercept is 7 for II

thus, the y-intercepts of given eq are not equal.

Answer 2

A) They have the same y intercept and the same rate of change

Explanation:

Write the equation for the line passing through the points (2,4) and (12,7)

Slope
`(7-4)/(12-2)` =
`(3)/(10)` = .3

y intercept (b)

y = mx + b

Use 2 fox x, 4 for y and .3 for m

y=mx + b

4 = .3(2) + b

4 = .6 + b Subtract .6 from both sides

3.4 = b

The equation is

y = .3x + 3.4

The two equation are identical so the slope and y intercepts are the same.