Question

Hi I need some help through this problem: Find the equation of a line parallel to 2x+4y-12=0 that passes through the point (-2,5).

equation in slope-intercept form.

Answer 1

y = -(1/2)x + 4

Explanation:

Lets look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = zero). Lets rewrite the given equation to conform to this format:

2x+4y-12=0

4y = -2x+12

y = -(2/4)x +(12/4)

y = -(1/2)x +3

This line has a slope of -(1/2). Parallel lines have the same slope as the reference line. So the new line will also have a slope of -(1/2) and we can write the new line equation as:

y = -(1/2)x + b

Any line with a slope of -(1/2) will be parallel. Any value of b is acceptable. But we want this line to intersect the point (-2,5), so we need to pick a value of b that forces the line through this point. To find the value of b to make that happen, enter the point (-2,5) in the parallel line equation from above:

y = -(1/2)x + b

5 = -(1/2)*(-2) + b for point (-2,5)

5 = 1+b

b = 4

The parallel line that intersects (-2,5) is

y = -(1/2)x + 4

See the attached graph.

Answer 2

y = -
`(1)/(2)` x + 4

Explanation:

the equation of a line in slope- intercept form is

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

given

2x + 4y - 12 = 0 ( subtract 2x - 12 from both sides )

4y = - 2x + 12 ( divide through by 4 )

y = -
`(2)/(4)` x +
`(12)/(4)`

y = -
`(1)/(2)` x + 3 ← in slope- intercept form

with slope m = -
`(1)/(2)`

• Parallel lines have equal slopes , then

y = -
`(1)/(2)` x + c ← is the partial equation of the parallel line

to find c substitute (- 2, 5 ) into the partial equation

5 = -
`(1)/(2)` (- 2) + c = 1 + c ( subtract 1 from both sides )

4 = c

y = -
`(1)/(2)` x + 4 ← equation of parallel line