Answer:
The first step is to find the gradient of the lines and the equation of the line is y = -2x + 6
Step-by-step explanation:
Given
Point 1 = (5,-4)
Point 2 = (-1,8)
Gradient, m = ∆y/∆x
∆y = y2 - y1
Where y2 = 8 and y1 = -4
∆y = 8 - -(4)
∆y = 8 + 4
∆y = 12
∆x = x2 - x1
Where x2 = -1 and x1 = 5
∆x = -1 - 5
∆x = -6
So, gradient, m = ∆y/∆x
m = 12/-6
m = -2
Calculating the equation of the line;
y - y1 = m(x - x1)
Or
y - y2 = m(x - x2)
Using any of the coordinates
Using first coordinate;
Point 1 = (5,-4)
x1 = 5 and y1 = -4
y - y1 = m(x - x1) becomes
y - -4 = -2(x - 5)
y + 4 = -2x + 10
Make y the subject of formula
y = -2x + 10 - 4
y = -2x + 6
Using the second coordinates
Point 2 = (-1,8)
Where y2 = 8 and x2 = -1
y - y2 = m(x - x2) becomes
y - 8 = -2(x - (-1))
y - 8 = -2(x + 1) -- open bracket
y - 8 = -2x -2 -- make y the subject of formula
y = -2x - 2 + 8
y = -2x + 6
Hence, the equation of the line is
y = -2x + 6
