Question

What is the equation of the line that is parallel to `y = 2x + 3` and passes through (-3,4)?

Answer 1

• Parallel Lines have the SAME SLOPE

• We first Find the Slope of the line `y=2x+3`
  The Slope Intercept Form of the equation of a given line is:
  `y = mx + c`
  where `m` is the Slope of that line, and `c` is the Y intercept.
  For this line, the Slope is `color(green)2`

• So the Slope of the line PARALLEL to `y=2x+3` will also be `color(green)2`. And we are given that it passes through the point `(-3,4)`
  With this, we can use the Point Slope form to find the equation of the line.

The Point-Slope form of the Equation of a Straight Line is:
`(y-k)=m*(x-h)`
`m` is the Slope of the Line

`(h,k)` are the co-ordinates of any point on that Line.

Here, we have been given the coordinates `(h,k)` of 1 point on that line as `(-3,4)`
And the Slope `m` is `color(green)2`

Substituting the values of `h, k and m` in the Point-Slope form, we get

`(y-4)=(2)*(x-(-3))`
The above will be the Equation of the Line in Point-Slope form.

• If we need it in the Slope Intercept Form, we need to follow these steps:

Modifying the equation, we get:

`(y-4) = 2*(x+3)`

`y-4= 2x+6`

`y=2x+6+4`

We get the equation of the line as :
`color(blue)( y=2x+10`

• The graph will look like this:

graph{y=2x+10 [-10, 10, -5, 5]}