Question

Compare the y-intercepts and the rates of change of the following items. y=3 a line which passes through the points (3,6) and (4,7).

A) the rates of change are the same, but the y-intercepts are different.
B)the y-intercepts are the same, but the rates of change are different.
C) the items have the same y-intercepts and the same rate of change.
D)the items have different y-intercepts and different rates of change.

Answer 1

B) The y-intercepts are the same (3), but the rates of change are different: option B.

How to compare equations of straight line.

Comparing the y-intercepts and rates of change,

let's find the slope (rate of change) and y-intercept for the given line.

The slope,m is calculated as (change in y) / (change in x):

m = 7 - 6/4 - 3

= 1

Let us use the slope and one of the given points (3,6)) to find the y-intercept (b) using the equation y = mx + b

6 = 1 *3 + b

b = 6-3

b = 3

So, the equation of the line is y = x + 3.

Now, comparing with the options:

B) The y-intercepts are the same (3), but the rates of change are different.

Therefore, the correct option is B.