If a line has a slope of 3 and contains the points (3, 1) and (5, y), then what is the value of y?

y = 7

giving the point (5, 7)

Step-by-step explanation:

Recall that the definition of slope is: rise/run. The rise is on the vertical y-axis and the run is on the horizontal x-axis. So a slope of "3" means that there is a rise of three units per unit of run in the horizontal axis. This means that if we start from the given point: (3, 1), moving one unit to the right (run) from x= 3 to x=4, the value of the y-coordinate should go up 3 units (from 1 to 4). Thus giving the point (4, 4). Now from here we can move another unit to the right (from 4 to 5 in x), and that would result in a rise of 3 units (from 4 to 7).

Therefore the new point on this line is: (5, 7)

Then we got the y-value that accompanies x = 5 on this line, by using its slope.