You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.

The rate of change at which the water level rises is centimeters per minute. So solving the equation for y gives a y-value equal to

Rise=16, run=7. Slope is rise/run, and therefore is 16/7. The run is considered to be the x coordinate. Since the x coordinate on the point is 21, we know it has moved 3 exact points away from the origin (21/7=3). We can use this movement of 3 exact points to determine the y coordinate as well. Since the rise (y) is 16 for every exact point on a graph, we know the graph has risen 48 units (16x3=48). So, the point ends up being (21,48). The rate of change is 16cm per 7 minutes, or 2.28cm/minute. The equation is Y=(16/7)X (no y intercept because the graph starts at the origin). The equation gives you the y value of 48 when x is equal to 21.