Question

Find the equation of the line that passes through (3,1) and is parallel to

y= 2 x + 3
.
Leave your answer in the form
y = m x + c

Answer 1

`y = 2x-5`

Explanation:

Given

`(x_1,y_1) = (3,1)`

Parallel to:
`y = 2x + 3`

Required

Determine the line equation

First, we calculate the slope of
`y = 2x + 3\\\\`

For an equation in the form
`y = mx + c`

`m = slope`

So, by comparison:

`m = 2`

The line equation is then calculated:

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

Where
`(x_1,y_1) = (3,1)` and
`m = 2`

So, we have:

`y - 1 = 2(x - 3)`

`y-1 = 2x-6`

`y = 2x-6+1`

`y = 2x-5`