Write the equation of the line that passes through the given points. ​(0​,2​) and ​(4​,16​)

The equation format for a straight line is y = mx + b, where m is the slope and b is the y-intercept, the value of y at x = 0. The slope is the rate of change of the line as x changes values. It is also termed the "rise over the run," of the difference in the value of y as x is changed.

We can calculate the rise/run from the two points. (0,2) and (-4,5). The rise is the difference between the two y values (5 - 2 = 3) and the run the difference in the x values (-4 - 0 = -4). Rise/run is therefore -3/4. This is "m" in the equation.

y = -(3/4)x + b

We need to find b. Input one of the points, (0,2) and solve for b.

2 = -(3/4)*0 + b
b = 2 (the line crosses the y axis when x = 0).

The full equation becomes:

y = -(3/4)x + 2