The given equation is:
[tex]7x+10y=-15[/tex]
a. To rewrite it in the form y=mx+b, let's solve it for y:
[tex]\begin{gathered} \text{Subtract 7x from both sides} \\ 7x+10y-7x=-7x-15 \\ 10y=-7x-15 \\ \text{Divide both sides by 10} \\ \frac{10y}{10}=\frac{-7x-15}{10} \\ y=\frac{-7x-15}{10} \\ \text{Apply the properties of fractions} \\ y=\frac{-7x}{10}-\frac{15}{10} \\ y=-\frac{7}{10}x-\frac{3}{2} \end{gathered}[/tex]
Then, the slope m=-7/10 and the y-intercept b=-3/2
b. In the above equation let x=10 and find y:
[tex]\begin{gathered} y=-\frac{7}{10}\cdot10-\frac{3}{2} \\ \text{Simplify} \\ y=-7-\frac{3}{2} \\ y=\frac{-7\cdot2-1\cdot3_{}}{1\cdot2} \\ y=\frac{-14-3}{2} \\ y=\frac{-17}{2} \\ y=-\frac{17}{2} \end{gathered}[/tex]
The ordered pair is:
[tex](10,-\frac{17}{2})[/tex]
