Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/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
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
