Question

A) Write the above equation in the form y=mx+b Enter the values of m and b in the appropriate boxes below as integers or reduced fractions (in the form A/B.)

Answer 1

The given equation is:

`7x+10y=-15`

a. To rewrite it in the form y=mx+b, let's solve it for y:

`\begin{gathered} \text{Subtract 7x from both sides} \\ 7x+10y-7x=-7x-15 \\ 10y=-7x-15 \\ \text{Divide both sides by 10} \\ (10y)/(10)=(-7x-15)/(10) \\ y=(-7x-15)/(10) \\ \text{Apply the properties of fractions} \\ y=(-7x)/(10)-(15)/(10) \\ y=-(7)/(10)x-(3)/(2) \end{gathered}`

Then, the slope m=-7/10 and the y-intercept b=-3/2

b. In the above equation let x=10 and find y:

`\begin{gathered} y=-(7)/(10)\cdot10-(3)/(2) \\ \text{Simplify} \\ y=-7-(3)/(2) \\ y=\frac{-7\cdot2-1\cdot3_{}}{1\cdot2} \\ y=(-14-3)/(2) \\ y=(-17)/(2) \\ y=-(17)/(2) \end{gathered}`

The ordered pair is:

`(10,-(17)/(2))`