Question

What is an equation of the line that is parallel to y=5x−7 and passes through (1, 11) ?

Answer 1

y = 5x+6 is equation of line that is parallel to y = 5x-7 and passing through (1,11).

Explanation:

We have given a equation of line and a point.

y = 5x-7 (x,y) = (1,11)

We have to find equation of line that is parallel to given equation of line and passing through given point.

y-y = m(x-x) is point-slope form of equation of line where m is slope of line.

Since, we know that parallel line have equal slope of line.

Given equation has slope equal to 5.

Parallel line also has slope equal to 5.

m = 5

Putting values in point-slope form of equation , we have

y-(11) = 5(x-1)

y-11 = 5x-5

y = 5x-5+11

y = 5x+6 is equation of line that is parallel to y = 5x-7 and passing through (1,11).

Answer 2

`y = 5x + 6`

EXPLANATION

The given equation is

`y = 5x - 7`

The slope of this line is

`m = 5`

Any line parallel to this line also has the same slope.

If the parallel line passes through (1,11),

then, it's equation is given by:

`y-y_1=m(x-x_1)`

Substitute the slope and point to get,

`y - 11 = 5(x - 1)`

`y = 5x - 5 + 11`

`y = 5 x + 6`

is the required equation.