Question

How do you graph `y=5x-5/2` using slope and intercept?

Answer 1

See below.

Explanation:

Use the general equation of a line:

`color(red)(y=mx+b)`

Here, `m` is the slope of the line. It states that, for every change in the `x` coordinate by `1` unit, the `y` coordinate changes by `m` units. Its formula is:

`(y_2-y_1)/(x_2-x_1)`.

Here, `m=5`.

`b` is the `y`-intercept, the value of `y` when the line intercepts the `y` axis. Here, the `b=-5/2`

Through the observations above, we find that:

• The line gets to `x=0` at `y=-5/2`
• After that, for every `1` unit increase in the `x` value, the `y` value increases by `5` units.

So at `x=0`, `y=-5/2`

At `x=1`, `y=5/2`

At `x=2`, `y=15/2`

At `x=3`, `y=25/2`

And so on and so forth. We can use Socratic's graphing utility to make sure of so:

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

We can see that our observations are true.