Function A and Function B are linear functions.

Question

Function A: y = x + 4
Function B: (4, 10), (-3, -10)
Which statement is true?
a. the y-value of Function A when x = -1 is greater than the y-value of Function B when x = -1
b. the y-value of Function A when x = -1 is less than the y-value of Function B when x = -1

Answer 1

To find the y-value of Function A when x = -1, we substitute x = -1 into the equation y = x + 4:

y = -1 + 4
y = 3

Therefore, the y-value of Function A when x = -1 is 3.

To find the y-value of Function B when x = -1, we first need to calculate the slope of the line passing through the points (4, 10) and (-3, -10):

Slope = (change in y) / (change in x)
Slope = (-10 - 10) / (-3 - 4)
Slope = -20 / -7
Slope = 20 / 7

Now we can find the equation of Function B in the form y = mx + c, where m is the slope and c is the y-intercept:

Using the point (4, 10):
10 = (20/7)(4) + c
10 = 80/7 + c
c = 10 - 80/7
c = 70/7 - 80/7
c = -10/7

Therefore, the equation of Function B is y = (20/7)x - 10/7. Now we substitute x = -1 into this equation to find the y-value of Function B:

y = (20/7)(-1) - 10/7
y = -20/7 - 10/7
y = -30/7
y = -4.2857 (rounded to four decimal places)

Comparing the y-values:
y (Function A, x = -1) = 3
y (Function B, x = -1) = -4.2857

Since 3 is greater than -4.2857, the statement "the y-value of Function A when x = -1 is greater than the y-value of Function B when x = -1" is true. Therefore, the correct answer is:

a. the y-value of Function A when x = -1 is greater than the y-value of Function B when x = -1