Question

How do you write the equation in point slope form given (1, 3) and (4, 4)?

Answer 1

`y=1/3x+8/3`

Explanation:

Recall that the equation for a line in point-slope form is `y=mx+b`, where m is the slope and b is the y-intercept.
First we have to find the slope using `m=(y-y_1)/(x-x_1)` (second point minus first point).
Plugging in (4,4) for (x,y) and (1,3) for `(x_1,y_1)`, we get `m=((4)-(3))/((4)-(1))=1/3`.
We now have the equation `y=1/3x+b`.
Next, let's plug in a point and solve for b. I will use the point (1,3).
`(3)=1/3(1)+b`
`b=3-1/3=9/3-1/3=8/3`.

With both our slope and y-intercept, we can now write the equation of the line as:
`y=1/3x+8/3`