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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 :

naǫ
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.

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