Question

Which linear function equation below would contain the points (-6,-8) and (12,4)
A)f(x)=2/3x+4
B)f(x)=f(x)=-2/3x+3
C)f(x)=f(x)=-2/3x-4
D)f(x)=f(x)=2/3x-4

Answer 1

To find the linear function that contains the points (-6, -8) and (12, 4), we first need to calculate the slope of the line using the two points.

The formula to find the slope m of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)

In this case, (-6, -8) corresponds to (x1, y1) and (12, 4) corresponds to (x2, y2):
m = (4 - (-8)) / (12 - (-6))
m = (4 + 8) / (12 + 6)
m = 12 / 18
m = 2 / 3

Now that we have the slope, we can substitute this value into the point-slope form of the linear function:
y - y1 = m(x - x1)

Using the point (-6, -8):
y - (-8) = (2/3)(x - (-6))
y + 8 = (2/3)(x + 6)

Then, we can simplify the equation further:
y + 8 = (2/3)x + 4
y = (2/3)x - 4

Therefore, the linear function equation that contains the points (-6, -8) and (12, 4) is:

D) f(x) = 2/3x - 4