Question

How do you graph `y=6x-3` by plotting points?

Answer 1

Plug in random values for `x`, then solve.

Explanation:

For example, let's pick `0`, `1`, and `2`.

`y=6(0)-3= -3`

`y=6(1)-3= 3`

`y=6(2)-3= 9`

Then just plot `(0, -3)`, (`1, 3)`, `(2, 9)` into a graph like so:

graph{y=6x-3 [-15, 15, -5, 10]}

Answer 2

See below

Explanation:

First of all, note that this function is a polynomial, because it can be written as a sum of powers of a variable with some coefficients:

`p(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n`

In your case, `n=1`, `a_0=-3` and `a_1=6`

And it is because `n=1` that this function is a line: every polyinomial of degree `1` represents a line.

To draw a line, you only need two points, so that you can connect them. To sample two points from the equation, you need to choose two points `x_1,x_2` and compute the respective images `y_1,y_2`. Then, draw them and connect the points `(x_1,y_1)` and `(x_2,y_2)`

Of course, it makes no sense to choose "difficult" points to compute, since any couple will work. For this reason, you may choose, for example, `x_1=0` and `x_2=1`, so that the computations will be easy:

`x_1=0 \implies y_1 = 6\cdot 0 - 3 = -3 \implies P_1 = (0,-3)`

`x_2=1 \implies y_1 = 6\cdot 1 - 3 = 3 \implies P_2 = (1,3)`

Now you only need to draw `P_1` and `P_2` and connect them.