Question

1. Complete the table with values for I or y that make this equation true: 3x + y = 15. 2. 6. 0 3 y 3 O 8. 2. Find the slope of the line

Answer 1

intoTo do this, you just have to plug the value of x or y into the equation and solve to get its corresponding x or y value. So,

*If x = 2

`\begin{gathered} 3x+y=15 \\ 3(2)+y=15 \\ 6+y=15 \\ \text{ Subtract 6 on both sides of the equation} \\ 6+y-6=15-6 \\ y=9 \\ \text{Then you have the pair (2,9)} \end{gathered}`

*If y = 3

`\begin{gathered} 3x+y=15 \\ 3x+3=15 \\ \text{ Subtract 3 on both sides of the equation} \\ 3x+3-3=15-3 \\ 3x=12 \\ \text{ Divide by 3 on both sides of the equation} \\ (3x)/(3)=(12)/(3) \\ x=4 \\ \text{ Then, you have the pair (4,3)} \end{gathered}`

*If x = 6

`\begin{gathered} 3x+y=15 \\ 3(6)+y=15 \\ 18+y=15 \\ \text{ Subtract 18 on both sides of the equation} \\ 18+y-18=15-18 \\ y=-3 \\ \text{Then, you have the pair (6,-3)} \end{gathered}`

*If x = 0

`\begin{gathered} 3x+y=15 \\ 3(0)+y=15 \\ y=15 \\ \text{Then, you have the pair (0,15)} \end{gathered}`

*If x = 3

`\begin{gathered} 3x+y=15 \\ 3(3)+y=15 \\ 9+y=15 \\ \text{ Subtract 9 on both sides of the equation} \\ 9-y-9=15-9 \\ y=6 \\ \text{ Then, you have the pair (3,6)} \end{gathered}`

*If y = 0

`\begin{gathered} 3x+y=15 \\ 3x+0=15 \\ 3x=15 \\ \text{ Divide by 3 into both sides of the equation} \\ (3x)/(3)=(15)/(3) \\ x=5 \\ \text{ Then, you have the pair (5,0)} \end{gathered}`

*If y = 8

`\begin{gathered} 3x+y=15 \\ 3x+8=15 \\ \text{ Subtract 8 on both sides of the equation} \\ 3x+8-8=15-8 \\ 3x=7 \\ \text{ Divide by 3 into both sides of the equation} \\ (3x)/(3)=(7)/(3) \\ x=(7)/(3)=2.3 \\ \text{ Then, you have the pair (2.3,8)} \end{gathered}`

Therefore, the table would be

Now, to find the slope of the line you can solve for y in the equation because that way you will have the equation of the line in its slope-intercept form, that is

`\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}`

So,

`\begin{gathered} 3x+y=15 \\ \text{ Subtract 3x on both sides of the equation} \\ 3x+y-3x=15-3x \\ y=15-3x \\ y=-3x+15 \end{gathered}`

Then, in this case

`\begin{gathered} y=mx+b \\ m=-3 \\ b=15 \end{gathered}`

Therefore, the slope of the line is -3.