ANSWER:
STEP-BY-STEP EXPLANATION:
The equation in its slope and intercept form has the following form:
[tex]\begin{gathered} y=mx+b \\ \\ \text{ where m is the slope and b is the y-intercetp} \\ \\ \text{ We calculate the slope as follows:} \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]
now, for each case we calculate the equation, as follows:
[tex]\begin{gathered} (1)\text{ }m=1,b=-3 \\ \\ y=x-3\rightarrow x-y=3 \\ \\ (2)\text{ }m=1,(-1,2) \\ \\ y=x+b\rightarrow2=-1+b\rightarrow b=3 \\ \\ y=x+3\rightarrow x-y=-3 \\ \\ (3)\text{ }(-2,3),(-3,4) \\ \\ m=\frac{4-3}{-3-(-2)}=\frac{1}{-3+2}=\frac{1}{-1}=-1 \\ \\ y=-x+b\rightarrow3=-(-2)+b\rightarrow b=1 \\ \\ y=-x+1\rightarrow y+x=1 \end{gathered}[/tex]
