Answer:
y=-3/2x+13
Step-by-step explanation:
Convert to slope-intercept form (y=mx+b):
-3x+2y=10
-3x-10+2y=0
-3x-10=-2y
-3/2x-5=y
y=-3/2x-5
Parallel lines have the same slope, so the slope of the equation will be m₁=m₂ where -3/2=-3/2
Solving for b, the y-intercept, we get:
y=-3/2x+b (Equation so far)
7=-3/2(4)+b [Plugging in (4,7)]
7=-12/2+b
7=-6+b
13=b
Therefore, the equation of the line that is parallel to the line -3x+2y=10 and goes through the point (4,7) is y=-3/2x+13
