Question

Determine the equation of each line

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 )

(a)

here m = -
`(3)/(4)` and c = 6, hence

y = -
`(3)/(4)` x + 6 ← equation of line

(b)

here m = 6, hence

y = 6x + c ← is the partial equation

to find c substitute (2, - 6 ) into the partial equation

- 6 = 12 + c ⇒ c = - 6 - 12 = - 18

y = 6x - 18 ← equation of line

(c)

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, 7)

m =
`(7-3)/(4+1)` =
`(4)/(5)`, hence

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

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

using (- 1, 3 ), then

3 = -
`(4)/(5)` + c → c = 3 +
`(4)/(5)` =
`(19)/(5)`

y =
`(4)/(5)` x +
`(19)/(5)` ← equation of line