SOLUTION: Find an equation of a straight line that passes through the point (2,3) and is parallel to the line with equation 3x + 4y -8 = 0

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Question 250706: Find an equation of a straight line that passes through the point (2,3) and is parallel to the line with equation 3x + 4y -8 = 0
Found 2 solutions by drk, JimboP1977:
Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
Step #1 - solve 3x + 4y -8 = 0 for y.
Y = -(3/4)X +2.
STEP #2 - find the slope based on the equation from STEP #1. M = (-3/4).
STEP #3 - parallel lines have the same slope. The slope you have from STEP #2 is the slope you want. m = (-3/4).
STEP #4 - using the slope from STEP #3, pick a point (2,3) and put those into
Y = mX + b. Solve for b.
3 = (-3/4)(2) + b.
b = 9/2.
STEP #5 - write the equation.
Y = (-3/4)X + 9/2.

Answer by JimboP1977(311) (Show Source):
You can put this solution on YOUR website!
First of all rearrange 3x+4y-8 = 0 into the form y=mx+c
4y = -3x+8
y = -3/4x + 2
Since we know that the second line is parallel to y = -3/4x + 2 then the gradient must be the same. The gradient is -3/4.
So we know that the second line is y=-3/4x + c . To find c we need to plug in the values of the point (2,3). 3 = -3/2 + c
Rearrange to find c = 3 + 3/2 = 9/2
So the equation is y = -3/4x + 9/2
If we plot the two lines we can see that they are parallel