Question

Write the equation of the line that passes through the points (4,-9) and (-5, 8). Put

your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

The equation of the line that passes through the points (4, -9) and (-5, 8) in fully simplified point-slope form is:

y = -17/9x - 13/9.

Explanation:

Formular:
y - y₁ = m(x - x₁),

where (x₁, y₁) is a point on the line, and m is the slope of the line.

m = (y₂ - y₁) / (x₂ - x₁),

where (x₁, y₁) = (4, -9) and (x₂, y₂) = (-5, 8):

m = (8 - (-9)) / (-5 - 4)

m = 17 / -9

m = -17/9.

y - (-9) = -17/9(x - 4)

y + 9 = -17/9(x - 4).

Simplified:

y + 9 = -17/9x + 68/9

y = -17/9x + 68/9 - 81/9

y = -17/9x - 13/9.