First,we will find the slope of the line
Using 8x - 6y = 5
we will have to re-arrange the equation above to be in the slope-intercept form.
That is; it should be in the form y = mx + b
8x - 6y = 5
6y = 8x -5
y = 8/6 x - 5/6
slope = 8/6 = 4/3
In a parellel equation the slope are the same, hence the slope of our new equation is 4/3
Next, we find the intercept of the new equation;
Using the point (-9, 1) and slope(m) = 4/3
we will substitute into the equation below and then solve for b, where b is the slope of our new equation
y = mx + b
1 = 4/3 (-9) + b
1 = 4(-3) + b
1 = - 12 + b
add 12 to both-side of the equation
1+ 12 = b
13 = b
b= 13
Substituting m = 4/3 and b = 13 into the formula; y = mx+ b
y = 4/3 x + 13
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