The Point-Slope form of the equation of a line is:
[tex]y_{}-y_1=m(x-x_1)_{}[/tex]
Where "m" is the slope of the line and this is a point on the line:
[tex](x_1,y_1)[/tex]
You can find the slope of a line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, knowing that this line passes through these points:
[tex](-2,-2);\mleft(2,1\mright)[/tex]
You can set up that:
[tex]\begin{gathered} y_2=-2 \\ y_1=1 \\ x_2=-2 \\ x_1=2 \end{gathered}[/tex]
Substituting values into the formula and evaluating, you get:
[tex]m=\frac{-2-1}{-2-2}=\frac{-3}{-4}=\frac{3}{4}[/tex]
Knowing the slope and coordinates of two points on the line, you can set up these two equations for this line:
1. First equation:
[tex]\begin{gathered} y-(-2)=\frac{3}{4}(x-(-2)) \\ \\ y+2=\frac{3}{4}(x+2) \end{gathered}[/tex]
2. Second equation:
[tex]y-1=\frac{3}{4}(x-2)[/tex]
The answers are: Option A and Option B.
