Question

How do you graph the equation `y=4x-2`?

Answer 1

The general equation for a line is `y = mx + b`, where:

• `y` is the dependent variable (dependent on `x`).
• `m = (y_2 - y_1)/(x_2 - x_1)` is the slope.
• `x` is the independent variable.
• `b` is the y-intercept.

Match that up to the general form:

`y = 4x - 2`

`=> m = 4`
`=> b = -2`

This means the slope describes an increase in `y` of `4` for every increase in `x` of `1`:

`m = (y_2 - y_1)/(x_2 - x_1) = 4/1`

This also means that the graph crosses the `y` axis at `y = -2`, the y-intercept where `x = 0`. This means that:

• `(0,-2)` is a point on the graph.
• Applying the slope onto `(0,-2)`, we get that `(0+1,-2+4) = (1,2)` is another point on the graph.

Two points make a line, so you have your graph:

graph{4x - 2 [-10, 10, -5, 5]}

And you should spot where `(1,2)` is on the graph to verify that it is there.