Question

Write an equation in slope-intercept form for the line through (-1, 1) and (0,3).

Answer 1

The slope intercept form of a line can be written as:

`y=mx+b`

where m is the slope and b is the y-intercept.

We have two points of the line: (-1,1) and (0,3).

Knowing that for x=0, the value of y=3 tells us that the y-intercept b is b=3:

`\begin{gathered} y=mx+b \\ 3=m\cdot0+b \\ 3=b \end{gathered}`

Using the other point and replacing the values of x and y in the equation we can calculate the value of the slope m:

`\begin{gathered} y=mx+3 \\ 1=m\cdot(-1)+3 \\ 1-3=-m \\ -2=-m \\ m=2 \end{gathered}`

Then, with m=2 and b=3, the equation becomes:

`y=2x+3`

Answer: y=2x+3