Question

How do you graph `y=4x+3` using a table?

Answer 1

Well, think of it this way: you plug in something for `x`, and you follow the expression `4x + 3` by multiplying by `4` then adding `3`, to get the corresponding output value `y`.

This equation is linear: `y = mx + b`,

where `m` is the slope (change in y over change in x) and `b` is the y-intercept (where it hits the `y` axis).

Your equation just has `m = 4` and `b = 3`.

So, let's make a quick table. You need at least two points to make a straight line, and three points to make a curve. Let's do five points though for practice.

`x = -2 -> y = 4(-2) + 3 = -5`
`x = -1 -> y = 4(-1) + 3 = -1`
`x = 0 -> y = 4(0) + 3 = 3`
`x = 1 -> y = 4(1) + 3 = 7`
`x = 2 -> y = 4(2) + 3 = 11`

In a table it then looks like this:

`color(white)([(color(black)(ul(y)),color(black)(ul("|")),color(black)(ul(x))),(color(black)(-5),color(black)(|),color(black)(-2)),(color(black)(-1),color(black)(|),color(black)(-1)),(color(black)(3),color(black)(|),color(black)(0)),(color(black)(7),color(black)(|),color(black)(1)),(color(black)(11),color(black)(|),color(black)(2))])`

And after plotting each point by looking at `x` and `y`, and moving to the right `x` units and up `y` units (if negative, move the opposite direction), we get:

graph{4x + 3 [-2, 2, -5, 11]}

If you look on this graph, you should be able to find every point we had on the table.