Question

What is the general form of the equation of the line shown?

Answer 1

the general form of the equation of the line will be:

`y-x=2`

Explanation:

Finding the slope:

Taking two points from the line as shown in figure

• (-2, 0)

• (0, 2)

Finding the slope between (-2, 0) and (0, 2)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)`

`m=(2-0)/(0-\left(-2\right))`

`m=1`

Finding the y-intercept

We know that the y-intercept can be calculated by setting x=0

From the figure, it is clear that at x=0, y=2

Thus, the y-intercept is (0, 2)

We know that the slope-intercept form of the equation line is:

`y=mx+b`

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

As we have already determined the slope = m = 1 and the y-intercept b=2.

Substituting the values in the slope-intercept form of the equation line

`y=mx+b`

`y=(1)x+2`

`y=x+2`

Writing the equation in the standard form form

As we know that the equation in the standard form is

`Ax+By=C`

where x and y are variables and A, B and C are constants

As we already know the equation in slope-intercept form

`y=x+2`

so just simplify the equation to write in standard form

`y-x=2`

Thus, the general form of the equation of the line will be:

`y-x=2`