Question

Using the following two points, what is the linear equation in standard and slope-intercept form? (5,-7), (-3,2)​

Answer 1

see explanation

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (5, - 7 ) and (x₂, y₂ ) = (- 3, 2 )

m =
`(2-(-7))/(-3-5)` =
`(2+7)/(-8)` = -
`(9)/(8)` , then

y = -
`(9)/(8)` x + c ← is the partial equation

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

using (- 3, 2 )

2 =
`(27)/(8)` + c ⇒ c = 2 -
`(27)/(8)` =
`(16)/(8)` -
`(27)/(8)` = -
`(11)/(8)`

y = -
`(9)/(8)` x -
`(11)/(8)` ← equation in slope- intercept form

multiply through by 8 to clear the fractions

8y = - 9x - 11 ( add 9x to both sides )

9x + 8y = - 11 ← equation in standard form