Question

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

What is the slope of the line represented by the equation y = x/3 - 5

1. Which ordered pairs make the equation true?

3x + 2y = –7

Choose all answers that are correct.
(Points : 1)
(–3, 1)
(–2, –1)
(1, –4)
(3, –8) this one has two answers
I already have the answers I just want to make sure its correct.

Answer 1

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


`10x+5y=4 \\ 5y=-10x+4 \\ y=-2x+(4)/(5) \\ m=\boxed{-2} \Leftarrow \hbox{the slope} \\ \\ y=(x)/(3)-5 \\ y=(1)/(3)x-5 \\ m=\boxed{(1)/(3)} \Leftarrow \hbox{the slope}`

2.

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


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


`(3,-8) \\ x=3 \\ y=-8 \\ \Downarrow \\ 3 * 3+2 * (-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.