Question

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

Answer 1

2x-y =-2

Explanation:

To find the equation of the line in standard form, first, we need to find the slope

m = ( y2-y1)/(x2-x1)

m = (10-2)/(4-0)

= 8/4 = 2

Then we can use the slope intercept form

y = mx+b where m is the slope and y is the y-intercept

y = 2x +b

Using the y-intercept ( 0,2)

y = 2x +2

The standard form is Ax +By =C where A is a positive integer and B is an integer

Subtract 2x from each side

-2x +y = 2

Multiply each side by -1

2x-y =-2

Answer 2

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 \\ \\ (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`