Question

Which linear graph represents a proportional relationship?

a graph of a line that passes through the points 0 comma 0 and 1 comma negative 3
a graph of a line that passes through the points 0 comma 2 and 1 comma 2
a graph of a line that passes through the points 0 comma negative 3 and 2 comma 1
a graph of a line that passes through the points 0 comma negative 1 and 2 comma negative 2

Answer 1

Points (0,0) and (1,-3) form a line that represents a proportional relationship.

Explanation:

A proportional relationship is one in which the ratio of x and y is always the same. (x/y) or (y/x) equals a constant, k.

Such a relationship will result in a straight line, if graphed. In a linear equation such as y = 2x, it can be seen that the ratio of y/x will always be 2 (or (1/2) for x/y).

But the straight line must go through the origin (0,0). If not, the relationship in no longer a constant, since the value of the y-intercept (b in y=mx+b) will cause deviations to a constant ratio of x and y.

See the attached graph. All points are marked, and equations for the lines connecting them are also plotted. Only the first set of points (0,0) and (1,-3) line on a straight line (Green line)with an intercept of (0,0), The other lines either have an intercept (Purple and Yellow) or have no relationship (Red Line: y is always equal to 2, regardless of the value of red)