Answer:
The equation of the line is:
[tex]y=(-\frac{1}{2})x+1[/tex]
Therefore, option a is the correct answer.
Step-by-step explanation:
Given the points
Finding the slope
[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,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)[/tex]
[tex]m=\frac{-1-2}{4-\left(-2\right)}[/tex]
[tex]m=-\frac{1}{2}[/tex]
As the point-slope form of the equation of the line is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope
substituting the values [tex]m=-\frac{1}{2}[/tex] and the point (-2, 2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y-2=\frac{-1}{2}\left(x+2\right)[/tex]
[tex]y-2=-\frac{1}{2}\left(x+2\right)[/tex] ∵[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
Add 2 to both sides
[tex]y-2+2=-\frac{1}{2}\left(x+2\right)+2[/tex]
[tex]y=(-\frac{1}{2})x+1[/tex]
Hence, the equation of the line is:
[tex]y=(-\frac{1}{2})x+1[/tex]
Therefore, option a is the correct answer.
