Question

Write an equation that describes the line
that passes through (2, 2) and (0, -3).

Answer 1

f(x) =
`(5)/(2)`x

Explanation:

The first thing we need to find is the slope of the line able to pass through the given two points. Right now we have y = mx + b (linear function equation) and we need to find m.

• Using the slope formula or
  `m = \frac{\text{rise}}{\text{run}} = (y_2 - y_1)/(x_2 - x_1)` and plugging in the given points' x and y values:

`(-3-2)/(0-2)` =
`(-5)/(-2)` =
`(5)/(2)`

• The slope of the line is that for every 5 units the line goes upwards, it goes 2 units to the right.

Our equation is now y =
`(5)/(2)`x + b. If you were in need of it, b gives the line's y-intercept, the place where it hits the y-axis. In this case you do not need b because the only specified conditions in the problem are the units the line hits.

Our final equation is:

f(x) =
`(5)/(2)`x