To find the equation that passes through (8,2)
and is parallel to the line 5x – 4y = 36
First, we need to find the slope (m) of the equation
To do that, we need to find the slope of the line;
5x – 4y = 36
To find the slope of the above, re-arrange the equation to be in the form
y= mx + b
where m is the slope and b is the intercept
5x – 4y = 36
-4y = -5x + 36
divide both-side of the equation by -4
y = 5/4 x - 9
From the above;
m = 5/4
Slope of parallel equations are the same
Hence the slope of our new equation is also 5/4
Now, we go ahead and find the intercept of our new equation
To do that, we need to substitute the points (8, 2) and m=5/4 into;
y=mx + b and then solve for b
That is;
2 = (5/4)(8) + b
2 = 10 + b
subtract 10 from both-side of the equation
2-10 = b
-8 = b
b= -8
Hence;
we can form the new equation by substituting m =5/4 and b = -8 into;
y=mx + b
That is;
y = 5/4 x -8
