PARCC Algebra II Creating Equations. Practice it free.

In slope-intercept form $y = mx + b$, the constant term $b$ is the $y$-intercept. Here $b = -9$.

The slope is $m = \dfrac{1 - (-3)}{4 - 0} = 1$. Because the line passes through $(0, -3)$, the $y$-intercept is $b = -3$ where $x = 0$. The equation is $y = x - 3$.

If the zeros are $x=-3$ and $x=-4$, that means the factors of the equation are $(x+3)$ and $(x+4)$. The product of these factors is $x^{2}+7x+12$. Comparing with $x^{2}+nx+12$, the missing linear coefficient is $n=7$.

The tomato plots use $4.5x$ square meters and the herb plots use $1.5y$ square meters. The total area used is $36$ square meters, so $4.5x + 1.5y = 36$.

Subtract the fourth-year salary from the first: $\text{\char36}54{,}600 - \text{\char36}48{,}000 = \text{\char36}6{,}600$. Over four years there are three equal raises, so divide by $4 - 1 = 3$ to get $x = \text{\char36}2{,}200$. Add $\text{\char36}2{,}200$ each year after the first: $\text{\char36}48{,}000$, $\text{\char36}50{,}200$, $\text{\char36}52{,}400$, $\text{\char36}54{,}600$. Sum all four years: $\text{\char36}205{,}200$.

More than $70$ means $s > 70$. At most $100$ means $s \le 100$, so $70 < s \le 100$.

A minimum means $p$ must be at least that value, so use $\ge\textsf{.}$ Four times $k$ plus $6$ is $4k + 6\textsf{,}$ giving $p \ge 4k + 6\textsf{.}$

The system is $2s + 4j = 50$ and $3s + j = 40\textsf{.}$ From the second equation, $j = 40 - 3s\textsf{.}$ Substitute into the first: $2s + 4(40 - 3s) = 50\textsf{,}$ so $2s + 160 - 12s = 50\textsf{,}$ $-10s = -110\textsf{,}$ $s = 11\textsf{,}$ and $j = 7\textsf{.}$