Question

How do you graph the line through point (2,6) and slope m=2/3?

Answer 1

See a solution process below:

Explanation:

First, we can plot the point given in the problem:

graph{((x-2)^2+(y-6)^2-0.1)=0 [-20, 20, -10, 10]}

Slope is `"rise"/"run"` or the change in the `y` values over the change in the `x` values:

The slope in the problem is `2/3`/3#

Therefore,

The change in the `"rise"` or `y` value is `color(red)(+2)`

The change in the `"run"` or `x` value is `color(blue)(+3)`

We can find another point by adding these to the values from the point in the problem:

`(2, 6) -> (2color(blue)(+ 3), 6color(red)(+2)) -> (5, 8)`

We can now plot this point:

graph{((x-2)^2+(y-6)^2-0.1)((x-5)^2+(y-8)^2-0.1)=0 [-20, 20, -10, 10]}

Now, we can draw a line through the two points:

graph{(y-2/3x - 4.6)((x-2)^2+(y-6)^2-0.1)((x-5)^2+(y-8)^2-0.1)=0 [-20, 20, -10, 10]}