ANSWER:
y = 2/3x + 2
EXPLANATION:
Write the equation in slope intercept form
y=mx+b
-2x+3y=2
3y=2+2x
y=2/3x+2/3
From the slope intercept form, we know that the slope is m=2/3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Substitute the slope 2/3 and the point (3,4) in the point slope form: y-y1=m(x-x1) which we get from m=y2-y1/x2-x1
y - (4) = 2/3 • (x-(3))
Simplify it
y - 4 = 2/3 • (x-3)
Solve for y
y - 4 = 2x/3 - 2
y = 2x/3 - 2 + 4
y = 2/3x + 2
