Answer:
f(x) = [tex]\frac{5}{2}[/tex]x
Step-by-step 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 [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex] and plugging in the given points' x and y values:
[tex]\frac{-3-2}{0-2}[/tex] = [tex]\frac{-5}{-2}[/tex] = [tex]\frac{5}{2}[/tex]
- 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 = [tex]\frac{5}{2}[/tex]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) = [tex]\frac{5}{2}[/tex]x
