Question

Which linear function equation would contain the points below?



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

Answer 1

To find the equation of the linear function, we need to find the slope and the y-intercept using the given points.

First, we find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (-6, -8) and (12, 4):
m = (4 - (-8)) / (12 - (-6))
m = (4 + 8) / (12 + 6)
m = 12 / 18
m = 2/3

So, the slope (m) is 2/3.

Next, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)

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

Finally, we can rearrange the equation to slope-intercept form (y = mx + b):
y + 8 = 2/3x + 4
y = 2/3x + 4 - 8
y = 2/3x - 4

Therefore, the linear function equation that contains the points (-6, -8) and (12, 4) is y = 2/3x - 4.