Question

Consider the line 8x-2y=-5.

Find the equation of the line that is parallel to this line and passes through the point (-4, 3).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 3).

Answer 1

4x - y = - 19 and x + 4y = 8

Explanation:

the equation of a line in slope- intercept form is

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

given

8x - 2y = - 5 ( subtract 8 from both sides )

- 2y = - 8x - 5 ( divide through by - 2 )

y = 4x +
`(5)/(2)` ← in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

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

3 = - 16 + c ⇒ c = 3 + 16 = 19

y = 4x + 19 ← equation of parallel line in slope- intercept form

subtract y from both sides

0 = 4x - y + 19 ( subtract 19 from both sides )

- 19 = 4x - y , that is

4x - y = - 19 ← equation in standard form

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given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(4)` , then

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

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

3 = 1 + c ⇒ c = 3 - 1 = 2

y = -
`(1)/(4)` x + 2 ← equation of perpendicular line in slope- intercept form

multiply through by 4 to clear the fraction

4y = - x + 8 ( add x to both sides )

x + 4y = 8 ← equation in standard form