Question

"Khalid is investigating two linear functions. The first linear function is defined by the equation

2x + 3y = 12. The second linear function passes through the points (3,-2) and(-2,8). What is the difference of the y-intercepts of the two functions? Enter your answer in the box below."

Answer 1

The difference of the y-intercepts of the two linear functions is 0, as both functions have the same y-intercept value of 4.

Step-by-step explanation:

Khalid is investigating two linear functions. To find the difference of the y-intercepts of the two functions, we need to put both equations in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

For the first linear function defined by 2x + 3y = 12, we isolate y to get:

3y = -2x + 12
y = (-2/3)x + 4

So, the y-intercept (b) for the first function is 4.

For the second linear function, we use the two points given, (3,-2) and (-2,8), to find the slope (m):

m = (y2 - y1) / (x2 - x1)
m = (8 - (-2)) / (-2 - 3)
m = 10 / -5
m = -2

Now, we can use the slope and one of the points to find the y-intercept. Let's use (3, -2):

y - y1 = m(x - x1)
-2 - (-2) = -2(3 - 3)
0 = 0

This confirms the slope is correct. Now we solve for b using the point:

-2 = -2(3) + b
b = -2 + 6
b = 4

So, the y-intercept for the second function is also 4. Therefore, the difference of the y-intercepts of the two functions is:

4 - 4 = 0

Thus, there is no difference in the y-intercepts of these two linear functions.