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

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 PointSlope form of the Equation of a Straight Line is:
Here, we have been given the coordinates
And the Slope
Substituting the values of
The above will be the Equation of the Line in PointSlope form.
 If we need it in the Slope Intercept Form, we need to follow these steps:
Modifying the equation, we get:
We get the equation of the line as :
 The graph will look like this:
graph{y=2x+10 [10, 10, 5, 5]}