Georgia Milestones Algebra I Creating Equations. Practice it free.

Point-slope form is $y - y_{1} = m(x - x_{1})\textsf{.}$ The slope is $m = 2$ and the point is $(3, 4)\textsf{,}$ so the equation is $y - 4 = 2(x - 3)\textsf{.}$

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

Subtract the fourth-year salary from the first: $\text{\char36}47{,}800 - \text{\char36}41{,}500 = \text{\char36}6{,}300$. Over four years there are three equal raises, so divide by $4 - 1 = 3$ to get $x = \text{\char36}2{,}100$. Add $\text{\char36}2{,}100$ each year after the first: $\text{\char36}41{,}500$, $\text{\char36}43{,}600$, $\text{\char36}45{,}700$, $\text{\char36}47{,}800$. Sum all four years: $\text{\char36}178{,}600$.

If the zeros are $x=5$ and $x=-4$, that means the factors of the equation are $(x-5)$ and $(x+4)$. The product of these factors is $x^{2}-x-20$. Comparing with $x^{2}-x+n$, the missing constant is $n=-20$.

Installing $x$ shrubs takes $1.8x$ hours and installing $y$ trees takes $3.2y$ hours. The total installation time is $22.4$ hours, so $1.8x + 3.2y = 22.4$.

More than $6$ means $p > 6$. At most $8$ means $p \le 8$, so $6 < p \le 8$.

The money equation is $4x + 6y = 22\textsf{.}$ Ticket counts must be whole numbers that are zero or greater. The pair $(4, 1)$ gives $4(4) + 6(1) = 22$ and both counts are whole and nonnegative.

Less than $15$ means the sum is strictly below $15\textsf{,}$ so $x + y < 15\textsf{.}$