Question 545257
Write the equation of the line containing the point (-2,6) and parallel(sp) to the line: 9x = 8y+5
First, find the slope of the given line by putting in the "slope-intercept" form y = mx+b:
9x = 8y+5 Subtract 5 from both sides.
9x-5 = 8y Now divide both sides by 8.
(9/8)x-5/8 = y  which you should write as:
y = (9/8)x-5/8 Now compare this with the "slope-intercept" form.
y = mx+b and you can see that the line represented by the given equation has a slope {{{m = 9/8}}}
Now, as you recall from your class, parallel lines have the same slope. This means that the new line whose equation you are going to write must have a slope of {{{m = 9/8}}}
So you can start the new equation, in "slope-intercept" form:
{{{y = (9/8)x+b}}} Now to find b, the y-intercept, you will use the coordinates of the given point (-2,6) and substitute the x- and y-coordinates into your starting equation above:
{{{y = (9/8)x+b}}} Substitute x = -2 and y = 6
{{{6 = (9/8)(-2)+b}}} Solve for b.
{{{6 = -9/4+b}}} Add {{{9/4}}} to both sides.
{{{8}}}{{{1/4 = b}}} Now you can complete your equation:
{{{y = (9/8)x+1/4}}}