Question

Find the equation of the line that passes through the point (-3,-4) and this parallel to the line that passes through the points (-5,1) and (7,-3)

Answer 1

y = -
`(1)/(3)` x - 5

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 ) = (-5,1) and (x₂, y₂ ) = (7, - 3)

m =
`(-3-1)/(7+5)` =
`(-4)/(12)` = -
`(1)/(3)`

• Parallel lines have equal slopes

hence
`m_(perpendicular)` = -
`(1)/(3)`, thus

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

T find c substitute (- 3, - 4) into the partial equation

- 4 = 1 + c ⇒ c = - 4 - 1 = - 5

y = -
`(1)/(3)` x - 5 ← equation of parallel line