Georgia Milestones Algebra II Creating Equations. Practice it free.

In slope-intercept form $y = mx + b$, the constant term $b$ is the $y$-intercept. Here $b = 7$.

The slope is $m = \dfrac{4 - 1}{6 - 2} = \dfrac{3}{4}$. Substitute $(2, 1)$: $1 = \dfrac{3}{4}(2) + b$, so $b = -\dfrac{1}{2}$. The equation is $y = \dfrac{3}{4}x - \dfrac{1}{2}$.

Subtract the fifth-year salary from the first: $\text{\char36}60{,}800 - \text{\char36}52{,}000 = \text{\char36}8{,}800$. Over five years there are four equal raises, so divide by $5 - 1 = 4$ to get $x = \text{\char36}2{,}200$. Add $\text{\char36}2{,}200$ each year after the first: $\text{\char36}52{,}000$, $\text{\char36}54{,}200$, $\text{\char36}56{,}400$, $\text{\char36}58{,}600$, $\text{\char36}60{,}800$. Sum all five years: $\text{\char36}282{,}000$.

If the zeros are $x=9$ and $x=-2$, that means the factors of the equation are $(x-9)$ and $(x+2)$. The product of these factors is $x^{2}-7x-18$. Comparing with $x^{2}+px-18$, the missing linear coefficient is $p=-7$.

Adult tickets contribute $18x$ dollars and child tickets contribute $7y$ dollars. The total amount collected is $516$ dollars, so $18x + 7y = 516$.

At least $2$ gives $d \ge 2$. Less than $7$ gives $d < 7$, so $2 \le d < 7$.

A minimum means $w$ must be at least that value, so use $\ge\textsf{.}$ Twice $n$ minus $12$ is $2n - 12\textsf{,}$ giving $w \ge 2n - 12\textsf{.}$

The system is $5c + 2b = 12$ and $2c + 6b = 10\textsf{.}$ Multiply the first equation by $3\textsf{:}$ $15c + 6b = 36\textsf{.}$ Subtract the second: $13c = 26\textsf{,}$ so $c = 2\textsf{.}$ Then $2(2) + 6b = 10\textsf{,}$ $6b = 6\textsf{,}$ and $b = 1\textsf{.}$