Question

What is the slope of the line represented by the equation 10x + 5y = 4?

Answer 1

1.
Convert the equations into the slope-intercept form y=mx+b.

$10x+5y=4 \\ 5y=-10x+4 \\ y=-2x+\frac{4}{5} \\ m=\boxed{-2} \Leftarrow \hbox{the slope} \\ \\ y=\frac{x}{3}-5 \\ y=\frac{1}{3}x-5 \\ m=\boxed{\frac{1}{3}} \Leftarrow \hbox{the slope}$

2.
$(-3,1) \\ x=-3 \\ y=1 \\ \Downarrow \\ 3 \times (-3)+2 \times 1 \stackrel{?}{=} -7 \\ -9+2 \stackrel{?}{=} -7 \\ -7 \stackrel{?}{=} -7 \\ -7 = -7 \\ \hbox{the ordered pair makes the equation true}$

$(-2,-1) \\ x=-2 \\ y=-1 \\ \Downarrow \\ 3 \times (-2) + 2 \times (-1) \stackrel{?}{=} -7 \\ -6-2 \stackrel{?}{=} -7 \\ -8 \stackrel{?}{=} -7 \\ -8 \not= -7 \\ \hbox{the ordered pair doesn't make the equation true}$

$(1,-4) \\ x=1 \\ y=-4 \\ \Downarrow \\ 3 \times 1+2 \times (-4) \stackrel{?}{=}-7 \\ 3-8 \stackrel{?}{=}-7 \\ -5 \stackrel{?}{=}-7 \\ -5 \not= -7 \\ \hbox{the ordered pair doesn't make the equation true}$

$(3,-8) \\ x=3 \\ y=-8 \\ \Downarrow \\ 3 \times 3+2 \times (-8) \stackrel{?}{=} -7 \\ 9-16 \stackrel{?}{=} -7 \\ -7 \stackrel{?}{=} -7 \\ -7 =-7 \\ \hbox{the ordered pair makes the equation true}$

The ordered pairs (-3,1) and (3,-8) make the equation true.