Answer:
the general form of the equation of the line will be:
[tex]y-x=2[/tex]
Step-by-step explanation:
Finding the slope:
Taking two points from the line as shown in figure
Finding the slope between (-2, 0) and (0, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]
[tex]m=\frac{2-0}{0-\left(-2\right)}[/tex]
[tex]m=1[/tex]
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:
[tex]y=mx+b[/tex]
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
[tex]y=mx+b[/tex]
[tex]y=(1)x+2[/tex]
[tex]y=x+2[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
As we already know the equation in slope-intercept form
[tex]y=x+2[/tex]
so just simplify the equation to write in standard form
[tex]y-x=2[/tex]
Thus, the general form of the equation of the line will be:
[tex]y-x=2[/tex]
