# The graph of a linear equation contains the points (3, 11), and (-2, 1). Which points also lies on the graph?

Sep 19, 2017

Any point on the graph $y = 2 x + 5$
For example, (2,9) or (1,7)

#### Explanation:

The graph of a linear equation usually takes place in the form of $y = m x + b$, where $m$ is the gradient, $b$ is the $y$-intercept, $y$ is the dependent value, and $x$ is the independent value. To write a linear equation given two points of $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$, we use the formula
$\frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = m$, where $m$ is the gradient.

Since we have the two points of (3,11) and (-2,1), we substitute them into the formula to get
$\frac{11 - 1}{3 - - 2} = m$

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

$2 = m$

So far our linear equation looks like this: $y = 2 x + b$
We now have to find $b$, and to do that we substitute in one of our known points (3,11) into the equation, like so:

$11 = 2 \cdot 3 + b$
$11 = 6 + b$
$5 = b$

Since $b = 5$, we now have our equation of $y = 2 x + 5$, which when graphed looks like this:
graph{y=2x+5 [-10, 10, -5.21, 5.21]}

To find other points on this graph simply locate them on the line, or complete the linear equation using different value of $x$ and $y$.

I hope I helped!