Question

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

Answer 1

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

Explanation:

The graph of a linear equation usually takes place in the form of `y=mx+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 `(x_1,y_1)` and `(x_2,y_2)`, we use the formula
`(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
`(11-1)/(3--2)=m`

`10/5=m`

`2=m`

So far our linear equation looks like this: `y=2x+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*3 + b`
`11=6+b`
`5=b`

Since `b=5`, we now have our equation of `y=2x+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!