Question

Write an equation that represents the line. Use exact numbers.​

Answer 1

y =
`(3)/(4)` x -
`(9)/(2)`

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 ) = (- 2, - 6) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line

m =
`(-3-(-6))/(2-(-2))` =
`(-3+6)/(2+2)` =
`(3)/(4)` , then

y =
`(3)/(4)` x + c ← is the partial equation

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

using (2, - 3 )

- 3 =
`(3)/(4)` (2) + c =
`(3)/(2)` + c ( subtract
`(3)/(2)` from both sides )

- 3 -
`(3)/(2)` + c , then

c = -
`(9)/(2)`

y =
`(3)/(4)` x -
`(9)/(2)` ← equation of line