1.
Convert the equations into the slope-intercept form y=mx+b.
[tex]10x+5y=4 \\
5y=-10x+4 \\
y=-2x+\frac{4}{5} \\
m=\boxed{-2} \Leftarrow \hbox{the slope} \\ \\
y=\frac{x}{3}-5 \\
y=\frac{1}{3}x-5 \\
m=\boxed{\frac{1}{3}} \Leftarrow \hbox{the slope}[/tex]
2.
[tex](-3,1) \\
x=-3 \\ y=1 \\ \Downarrow \\
3 \times (-3)+2 \times 1 \stackrel{?}{=} -7 \\
-9+2 \stackrel{?}{=} -7 \\
-7 \stackrel{?}{=} -7 \\
-7 = -7 \\
\hbox{the ordered pair makes the equation true}[/tex]
[tex](-2,-1) \\
x=-2 \\ y=-1 \\ \Downarrow \\
3 \times (-2) + 2 \times (-1) \stackrel{?}{=} -7 \\
-6-2 \stackrel{?}{=} -7 \\
-8 \stackrel{?}{=} -7 \\
-8 \not= -7 \\
\hbox{the ordered pair doesn't make the equation true}[/tex]
[tex](1,-4) \\
x=1 \\ y=-4 \\ \Downarrow \\
3 \times 1+2 \times (-4) \stackrel{?}{=}-7 \\
3-8 \stackrel{?}{=}-7 \\
-5 \stackrel{?}{=}-7 \\
-5 \not= -7 \\
\hbox{the ordered pair doesn't make the equation true}[/tex]
[tex](3,-8) \\
x=3 \\ y=-8 \\ \Downarrow \\
3 \times 3+2 \times (-8) \stackrel{?}{=} -7 \\
9-16 \stackrel{?}{=} -7 \\
-7 \stackrel{?}{=} -7 \\
-7 =-7 \\
\hbox{the ordered pair makes the equation true}
[/tex]
The ordered pairs (-3,1) and (3,-8) make the equation true.