Question

Find the equation of this line please

Answer 1

y =
`(3)/(4)` x + 14

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 ) = (- 3, - 2) and (x₂, y₂ ) = (5, 4) ← 2 points on the line

m =
`(4-(-2))/(5-(-3))` =
`(4+2)/(5+3)` =
`(6)/(8)` =
`(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 (5, 4 )

4 =
`(3)/(4)` (5) + c =
`(15)/(4)` + c ( subtract
`(15)/(4)` from both sides )

4 -
`(15)/(4)` = c , then

c =
`(16)/(4)` -
`(15)/(4)` =
`(1)/(4)`

y =
`(3)/(4)` x +
`(1)/(4)` ← equation of line