Question

3. Find an equation of a line through (0, −7) and parallel to the line y = 1 / 2 x + 5.

a. What is the slope of any line parallel to the given line? Explain your answer.
b. Write an equation of a line through the point and parallel to the line.
c. If a line is perpendicular to y = 1 / 2 x + 5, will it be perpendicular to x − 2y = 14? Explain.

Answer 1

the slope of any line parallel to the given line is
`(1)/(2)`

`y=(1)/(2)x-7`

perpendicular

Explanation:

line
`y = (1)/(2)x + 5`

Slope of the given line is 1/2

Slope of parallel lines are same

the slope of any line parallel to the given line is
`(1)/(2)`

Equation of a line is y=mx+b

`y-y1=m(x-x1)`

m=1/2 (x1,y1) is (0.-7)

`y-y1=m(x-x1)`

`y+7=(1)/(2)(x-0)`

`y=(1)/(2)x-7`

`x - 2y = 14`

Subtract x from both sides

`- 2y = -x+14`

Divide both sides by -2

`y=(1)/(2)x-7`

slope of both lines are same so they are parallel.

So the line is perpendicular to
`x - 2y = 14`