Identifying Functions
Function rules from equations - Questions
Answers
1. \(y=5 x-26\)
To arrive at a correct equation, we have to solve the equation for \(y\).
\(\begin{aligned}
y+6 &=5(x-4) \\
y &=5(x-4)-6 \\
y &=5 x-20-6 \\
y &=5 x-26
\end{aligned}\)
The following equation is rearranged so \(x\) is the independent variable:
\(y=5 x-26\)
2. \(b=2-\frac{3}{4} a\)
To arrive at a correct equation, we have to solve the equation for \(b\).
\(\begin{aligned}
3 a-7 &=-4 b+1 \\
4 b-1 &=7-3 a \\
4 b &=8-3 a \\
b &=\frac{8}{4}-\frac{3 a}{4} \\
b &=2-\frac{3}{4} a
\end{aligned}\)
The following equation is rearranged so \(a\) is the independent variable:
\(b=2-\frac{3}{4} a\)
3. \(w=-\frac{7}{6} u\)
To arrive at a correct equation, we have to solve the equation for \(w\).
\(\begin{aligned}
4 u+8 w &=-3 u+2 w \\
6 w &=-7 u \\
w &=\frac{-7 u}{6} \\
w &=-\frac{7}{6} u
\end{aligned}\)
The following equation is rearranged so \(u\) is the independent variable:
\(w=-\frac{7}{6} u\)
4. \(q=6 r+16\)
To arrive at a correct equation, we have to solve the equation for \(q\).
\(\begin{aligned}
q-10 &=6(r+1) \\
q &=6(r+1)+10 \\
q &=6 r+6+10 \\
q &=6 r+16
\end{aligned}\)
The following equation is rearranged so \(r\) is the independent variable:
\(q=6 r+16\)