Question

How do you solve `2x+22=0` by graphing?

Answer 1

Plot the graph of `(2x+22)`.
The solution is the value of `x` where the line crosses the `x` axis.

Explanation:

It is very easy to solve this by using algebra, but if you need to solve it by graphing then:

Plot the graph of `(2x+22)`.
The solution is the value of `x` where 2`x`+22 = 0 (i.e. where the line crosses the `x` axis).

You can do this with a graphic calculator or computer, or you can do it on paper as follows:

Put values for `x` into the left hand side of the eqn
(`2x+22`) ....(you should recognize this as a straight line)

and plot them as the `y` value on a graph

e.g.
if `x` = 0, `y = (2*0)+22 = 22` so plot the point (0,22)
if `x` = 4, `y = (2*4)+22 = 30` so plot the point (4,30)
if `x` = -6, `y = (2*-6)+22 = 10` so plot the point (-6,10)

Draw a straight line through these points:
graph{2x+22 [-41.3, 38.7, -5.58, 34.42]}

The line shows all the values of `2x+22` (read on `y` axis) for all values of `x` (`x` axis)

We are interested in the value of `x` when `2x+22=0`, so read the value of `x` at `y = 0` (where the line crosses the `x` axis).

Looks like it's `x=-11`

(We can check this by using `x= -11` in the expression 2`x`+22 and verifying that it is equal to 0 for this value of `x`)

`2*-11+22= -22 + 22 = 0`

The plot of `x=-11` on a graph is a vertical line through x=-11
graph{-1000x-11000 [-41.3, 38.7, -5.58, 34.42]}