Question

Write the equation of the line with the points (0, 2) and (4, 10) in standard form.

Answer 1

By definition, the of a line written in Standard form is:

$Ax+By=C$

Where "A", "B" and "C" are Integers ("A" is positive).

The Slope-Intercept form of the equation of a line is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

You know that this line passes through these points:

$(0,2);(4,10)$

By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:

$b=2$

Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":

$y=mx+b$

Then, the slope of the line is:

$\begin{gathered} 10=m(4)+2 \\ 10-2=4m \\ 8=4m \\ \\ \frac{8}{4}=m \\ \\ m=2 \end{gathered}$

Therefore, the equation of this line in Slope-Intercept form is:

$y=2x+2$

To write it in Standard form, you can follow these steps:

- Subtract 2 from both sides of the equation:

$\begin{gathered} y-(2)=2x+2-(2) \\ y-2=2x \\ \end{gathered}$

- Subtract "y" from both sides of the equation:

$\begin{gathered} y-2-(y)=2x-(y) \\ -2=2x-y \\ 2x-y=-2 \end{gathered}$

The answer is:

$2x-y=-2$