Question

Write an equation of a line parallel to y=1/2x - 5 that contains (4, 6).

Answer 1

Answer: y = –(3/4)x + 2.75

Explanation:

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = –3x + 12

y = –(3/4)x + 3

slope = –3/4

We know that the second line will also have a slope of –3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = –3/4(1) + b

2 = –3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75

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 )

y =
`(1)/(2)` x - 5 ← is in slope- intercept form

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

• Parallel lines have equal slopes , then

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

to find c substitute (4, 6 ) into the partial equation

6 = 2 + c ⇒ c = 6 - 2 = 4

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