Question

Write the slope-intercept form of the line that passes through (-10,17) and (5,-4)

Answer 1

y = -
`(7)/(5)` x + 3

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 10, 17) and (x₂, y₂ ) = (5, - 4)

m =
`(-4-17)/(5+10)` =
`(-21)/(15)` = -
`(7)/(5)`

y = -
`(7)/(5)` x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 4), then

- 4 = - 7 + c ⇒ c = - 4 + 7 = 3

y = -
`(7)/(5)` x + 3 ← in slope-intercept form