Question

If a line passes through the points (1, 3) and (0, 0), what is the equation of the line?

Answer 1

`y=3x`

Explanation:

Use the slope formula to first determine the slope:
`m=(y_2-y_1)/(x_2-x_1)`

If we let `(1,3)->(color(blue)(x_1),color(red)(y_1)) and (0,0) -> (color(blue)(x_2),color(red)(y_2))` then,

`m=(color(red)(0)color(blue)(-3))/(color(red)(0)color(blue)(-1)` `=(-3)/-1=3`

Now that we know our slope is `3` we can find the equation of the line by using the slope and any of the two points given into the point-slope formula: `y-y_1=m(x-x_1)` I will use `(0,0)`

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

We then simplify and write in terms of `y=mx+b`

`y=3x-0->y=3x`

Graphically, the equation looks like this: (You can actually interact with the graph with your mouse and you'll see that the line does in fact go through the points `(0,0)` and `(1,3)` graph{3x [-10, 10, -5, 5]}