# The graph of a linear equation contains the points (3.11) and (-2,1). Which point also lies on the graph?

May 12, 2018

(0, 5) [y-intercept], or any point on the graph below

#### Explanation:

First, find the slope with two points by using this equation:

$\frac{{Y}_{2} - {Y}_{1}}{{X}_{2} - {X}_{1}}$ = $m$, the slope

Label your ordered pairs.

(3, 11) $\left({X}_{1} , {Y}_{1}\right)$
(-2, 1) $\left({X}_{2} , {Y}_{2}\right)$

Plug in your variables.

$\frac{1 - 11}{- 2 - 3}$ = $m$

Simplify.

$\frac{- 10}{- 5}$ = $m$

Because two negatives divide to make a positive, your answer will be:

$2$ = $m$

Part Two

Now, use point-slope formula to figure out what your equation in y = mx + b form is:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Plug in your variables.

$y - 11 = 2 \left(x - 3\right)$

Distribute and simplify.

$y - 11 = 2 x - 6$

Solve for each variable. To solve for the y = mx + b equation, add 11 to both sides to negate -11.

$y = 2 x + 5$

Now, plot this on a graph:

graph{2x + 5 [-10, 10, -5, 5]}