Question

What is the slope-intercept equation for the line below?

Answer 1

Answer:

$y=\frac{2}{5}x+2$

Step-by-step explanation:

(x1, y1) = (5, 4)

(x2, y2) = (0, 2)

First, find the slope. The slope formula is:

$m=\frac{y2-y1}{x2-x1}$

I marked the 2 points above in that form, so you can plug those in here:

$m=\frac{2-4}{0-5}\\\\m=\frac{-2}{-5}\\\\m=\frac{2}{5}$

The slope of this line is 2/5. Next, you can use that slope and whichever known point you want to find the y-intercept. Slope-intercept form is:

$y=mx+b$

where m is the slope and b is the y-intercept.

Plug in the slope we found for m and whichever point you want for (x, y):

$2=\frac{2}{5}0+b$

Now, solve for b:

$2=0+b\\b=2$

In this particular case, there wasn't much to be done. We already had a point at x = 0, and that is already our y-intercept. For similar problems though, that's how you would do it.

Finally, with both the slope and the y-intercept, you can write the equation:

$y=\frac{2}{5}x+2$