Question

Which can be the first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form?

Answer 1

Hello : let A(5,-4) B(-1,8)
the slope is : (YB - YA)/(XB -XA)
(8+4)/(-1-5) =-2
an equation is : y=ax+b a is a slope

y = -2x +b

the line through point A(5,-4) : -4= -2(5)+b
b = 6
the equation is : y =-2x+6

Answer 2

The first step is to find the gradient of the lines and the equation of the line is y = -2x + 6

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