Question

How do you graph `y = 3x + 5`?

Answer 1

graph{3x+5 [-10, 10, -5, 5]}

`x` intercept: `x=-5/3`
`y` intercept: `y=5`

Explanation:

For a linear graph, the quickest way to sketch the function is to determine the `x` and `y` intercepts and draw a line between the two: this line is our graph.

Let's calculate the `y` intercept first:

With any function, `y` intercepts where `x = 0`.
Therefore, substituting `x = 0` into the equation, we get:

`y=3*0+5`
`y=5`
Therefore, the `y` intercept cuts through the point (0,5)

Let's calculate the `x` intercept next:

Recall that with any function: `y` intercepts where `x = 0`.

The opposite is also true: with any function `x` intercepts where `y = 0`.

If we substitute `y = 0`, we get:

`0=3x+5`
Let's now rearrange and solve for `x` to calculate the `x` intercept.

`-5=3x`
`-5/3=x`
Therefore, the `x` intercept cuts through the point `(-5/3,0)`.

Now we have both the `x` and `y` intercepts, all we have to do is essentially plot both intercepts on a set of axis and draw a line between them

The graph of the function `y=3x+5`:

graph{3x+5 [-10, 10, -5, 5]}