Question

Determine a system of linear equations for the tables below.

Answer 1

A. y - 10 = 6(x - 2)

y - 20 = -2(x + 3)

Explanation:

The first equation given the following points (-2, -14) and (2, 10):

Slope (m) = ∆y/∆x = (10 -(-14)) / (2 - (-2)) = 24/4= 6

Using the highlighted point and the slope, we can write an equation for this by substituting (a, b) = (2, 10) and m = 6 into y - b = m(x - a)

Thus:

y - 10 = 6(x - 2)

The second equation given the following points (-3, 20) and (5, 4):

Slope (m) = ∆y/∆x = (4 - 20) / (5 - (-3)) = -16/8 = -2

Using the highlighted point and the slope, we can write an equation for this by substituting (a, b) = (-3, 20) and m = -2 into y - b = m(x - a)

Thus:

y - 20 = -2(x - (-3))

y - 20 = -2(x + 3)