A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3). Which equation represents the graphed function? –3x + 2 = y –x + 2 = y x – 3 = y 2x – 3 = y

Accepted Solution

Answer:not any of the given lines go through those three pointsStep-by-step explanation:We recall that if a line passes through a given point, that means that the equation of such line renders an equality when we replace the (x, y) pairs of values given in the equation.For the following equations of lines:[tex]\\-x+2=y\\x-3=y\\2x-3=y[/tex]one can replace the values for x and y given in the points on the plane (0,-3), (2,0) and (4,3)and find which is the only line that gives true statements for all of them:The first line doesn't give a true statement just with the first point on the plane  (0,-3)notice that [tex]-3x+2=y\\-3(0)+2\neq -3\\2\neq -3[/tex]Something similar happens with the second given line, so that line is not the appropriate one.The third and fourth lines give both a true statement for the point (0,-3):[tex]x-3=y\\(0)-3=-3\\-3=-3[/tex] and [tex]2x-3=y\\2(0)-3=-3\\-3=-3[/tex]So we need to check another point with those lines to determine which is the correct one. Let's use (2,0):[tex]x-3=y\\(2)-3\neq 0\\-1\neq 0[/tex] and  [tex]2x-3=y\\2(2)-3\neq 0\\1\neq 0[/tex]Therefore none of the given lines go through all of the given points, and don't represent the real line that does.