graph the equation by plotting three points. if all three are correct, the line will appear. -3y=5x-7

Accepted Solution

Answer: (x, y) = (-1, 4), (2, -1), (5, -6)Step-by-step explanation:You can choose any value you like for either x or y, then solve for the other value. I like to plot points with integer coefficients, so I would look for sets of those.The nature of this equation is that it will have integer solutions with x-values spaced 3 apart and y-values spaced 5 apart. (The spacing of each corresponds to the coefficient of the other.) So, the trick is to find an x-value that gives an integer solution for y. (You will need to try at most 3 consecutive integers.)Solving the equation for y, we get ... y = -5/3x +7/3Right away, we know that x=0 will not give an integer solution for y. Nor does x=1. The third consecutive integer that is easy to try is x = -1, so ... y = (-5/3)(-1) +7/3 = (5+7)/3 = 4 . . . . an integer value for yOur first point is then (x, y) = (-1, 4).Since the slope is negative, we know that increasing x will decrease y. Thus we can simply add (3, -5) to any point to get another point on the line.Two more points on the line are ... (-1, 4) +(3, -5) = (2, -1) (2, -1) +(3, -5) = (5, -6)Three integer-valued points on this line are (-1, 4), (2, -1), (5, -6).