Question

Find the STANDARD FORM equation of a line with y-intercept=2 that passes through the point (2,4) SHOW ALL WORK.

Answer 1

To solve this problem it's easier to first find the y-intercept form instead of the standard one, and then re-arrange it in the standard form. The y-intercept form is given below:

`y=m\cdot x+b`

Where "m" is the slope of the line and "b" is the y-intercept. The problem already informed us of the value of "b", therefore we can use the known point to find the value of "m".

`\begin{gathered} y=m\cdot x+2 \\ 4=m\cdot2+2 \\ m\cdot2=4-2 \\ m\cdot2=2 \\ m=(2)/(2)=1 \end{gathered}`

We now have the slope-intercept line as shown below:

`y=x+2`

We need to re-arrange it in the standard form, which is shown below:

`A\cdot x+B\cdot x=C`

Where A,B and C are constants. So we need to isolate the two variables, x and y, on the left side of the equation.

`-x+y=2`