Question

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

Answer 1

To find the equation of a linear function, we can use the slope-intercept form, which is given as y = mx + b, where m represents the slope and b represents the y-intercept.

To determine the equation that contains the points (-6, -8) and (12, 4), we need to calculate the slope first.

The slope (m) is given by the formula: m = (y₂ - y₁) / (x₂ - x₁)

For the given points (-6, -8) and (12, 4), the slope is:
m = (4 - (-8)) / (12 - (-6))
= 12 / 18
= 2/3

Since the slope (m) is 2/3, and we have one of the points (-6, -8), we can substitute these values into the slope-intercept form (y = mx + b) to solve for b:

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

Therefore, the equation of the linear function is F(x) = 2/3x - 4.

So, the correct answer is F(x) = 2/3x - 4.