Question

Write the equation of the linear function that passes through the points ( 2, −3) and ( −8, 5).

Answer 1

First, let's find the slope of the line:

m = (5 - (-3)) / (-8 - 2)
m = 8 / -10
m = -4/5

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the first point (2, -3):

y - (-3) = -4/5(x - 2)
y + 3 = -4/5(x - 2)

Now, simplify the equation:

y + 3 = -4/5x + 8/5
y = -4/5x + 8/5 - 15/5
y = -4/5x - 7/5

Therefore, the equation of the linear function that passes through the points (2, −3) and (−8, 5) is y = -4/5x - 7/5.