Question

What is an equation of the line that passes through the points (4, -2) and (2, 3)?

Answer 1

Step-by-step explanation:

For this problem, you'll need two formulas:

Slope: y1 - y2/x1 - x2

Point Slope: y - y1 = m(x - x1)

First thing you need to use is the slope formula.

Plugging in your coordinates gives you:

$\frac{-2-3}{4-2}$ = $\frac{-5}{-2}$

You can simplify this by getting rid of the negatives since two negatives make a positive.

Now to use the point slope formula.

For this formula, the slope we just found, $\frac{5}{2}$, replaces the m, and for the x1 and y1, you use one of the original points(either (4,-2) or (2,3)).

I'll be using the point (2,3). Now plug everything in:

$y-3=\frac{5}{2} (x-2)$

First thing you should do is distribute the $\frac{5}{2}$:

$y-3=\frac{5}{2} x-5$

Next thing to do is get the y by itself by adding 3 to both sides, which gives you your answer of:

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

Hope this was helpful, good luck :)