a) Here you have received a slope m = 3/2 and an intercept b = 4 where the line hits the y axis.
So with this information you should choose to use the slope intercept formula (y = mx + b )to find the equation of the line.
if you plug in the coreesponding values you will get the equation y = (3/2)x + 4.
b) You have two points given.
So using the the 2 point slope formula y - y1 = [(y2 - y1)/(x2 - x1)](x - x1) is best. Your 2 points P1 and P2 have the form: P1 = (x1, y1) = (3, -4) and P2 = (x1, y1) = (0, 4). So now you plug in all the corresponding values:
y - (-4) = [(4 - (-4))/(0 - 3)](x - 3) next simplify
y + 4 = (-8/3)(x - 3) distribute the -8/3 and you will see immediately the 3 's cancel out so you have
y + 4 = (-8/3)x + 8 Last substract 4 from both sides of the equation
y = (-8/3)x + 4 Tada! this is the equation of your line.
c) For this one you are given a point P1 = (x1, y1) = (-2.5, 4) and a slope m = 2.
So using the point slope formula y - y1 = m(x - x1) is best.
So plug in: y - 4 = 2(x - (-2.5))
Now simplify: y - 4 = 2x + 5
And solve: y = 2x + 5 + 4 which is the same as y = 2x + 9 Tada! there is your answer.
Hope I helped :)