Question

Which linear function equation would contain the points below?



(-6,-8) and (12,4)

f(x)=2/3x+4

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

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

f(x)=2/3x-4

Answer 1

To find the linear function equation that contains the points (-6,-8) and (12,4), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, let's calculate the slope (m) using the formula:

m = (y2 - y1)/(x2 - x1)

Let's plug in the values for our two points:

m = (4 - (-8))/(12 - (-6))
m = (4 + 8)/(12 + 6)
m = 12/18
m = 2/3

Now that we have the slope, we can plug it into the equation:

f(x) = (2/3)x + b

To find the y-intercept (b), we can substitute the coordinates of either point into the equation. Let's use the first point (-6,-8):

-8 = (2/3)(-6) + b
-8 = -12/3 + b
-8 = -4 + b
b = -4 + 8
b = 4

Now we have determined the slope (m = 2/3) and the y-intercept (b = 4), so the equation of the linear function that contains the points (-6,-8) and (12,4) is:

f(x) = (2/3)x + 4

Therefore, the correct answer is f(x) = (2/3)x + 4.