Consider a line passing through the following points:
[tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex]
Than the its slope a and its intercept b can be expressed as:
[tex]\begin{gathered} a=\frac{y_2-y_1}{x_2-x_1} \\ b=y_1-ax_1=y_2-ax_2 \end{gathered}[/tex]
Then, for a line passing through the points (-2,-4) and (3,1), its slope and intercept are given by:
[tex]\begin{gathered} a=\frac{1-(-4)}{3-(-2)}=\frac{5}{5}=1 \\ b=-4-(-2)=1-3=-2 \end{gathered}[/tex]
Therefore, the equation for this line in the slope-intercept form is given by:
[tex]y=x-2[/tex]
Now, we must rewrite equations A, B, C and D in the slope-intercept form and check whose are correct:
[tex]\begin{gathered} A) \\ y+4=x+2 \\ y+4-4=x+2-4 \\ y=x-2 \\ \text{Correct} \\ B) \\ y-1=x-3 \\ y-1+1=x-3+1 \\ y=x-2 \\ \text{Correct} \\ C) \\ y=-x-2 \\ \text{Wrong} \\ D) \\ y=x-2 \\ \text{Correct} \end{gathered}[/tex]
Answer: A, B and D
