Georgia Milestones Algebra I Creating Equations Practice

Creating Equations skills

Create equations that describe numbers or relationships

Create equations in two or more variables to represent relationships

Create inequalities in one variable and use them to solve problems

Standards basis

Georgia Standards of Excellence (state-adopted content standards) — Georgia

How the Georgia Milestones reports it

Georgia Milestones is Georgia’s own statewide assessment system, aligned to Georgia’s state-adopted content standards rather than a shared national test framework. The official page says it measures knowledge and skills in the state-adopted standards for mathematics across grades 3 through high school ([Georgia Department of Education](https://gadoe.org/assessment-accountability/georgia-milestones/)).

Blueprint & weighting

Not published on the official Georgia Milestones overview page reviewed here.

Official sources

Georgia Department of Education

8 free questions · 0/0 correct

Practice playeasy

In $y = 3x + 1$ , what is the slope?

In slope-intercept form $y = mx + b$ , the coefficient of $x$ is the slope. Here $m = 3$ .

Practice playmedium

A line passes through the points $(-1, 4)$ and $(2, -2)$ . Which equation represents this line in slope-intercept form?

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

Practice playmedium

Priya earns $\text{\char36}41{,}500$ in her first year as a librarian. She receives the same dollar raise each year and earns $\text{\char36}47{,}800$ in her fourth year. What is the total of Priya's earnings over her four years at the library?

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: $\text{\char36}178{,}600$ .

Practice playmedium

What value of $n$ makes the solutions of $x^{2}-x+n=0$ be $x=5$ and $x=-4$ ?

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 $n=-20$ .

Practice playmedium

A landscaper plants shrubs that each take $1.8$ hours to install and trees that each take $3.2$ hours to install. The landscaper spends a total of $22.4$ hours installing $x$ shrubs and $y$ trees. Which equation represents this situation?

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

Practice playmedium

A science lab classifies a liquid as neutral when its pH level $p$ is more than $6$ but at most $8$ . Which inequality represents the possible values of $p$ ?

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

Practice playeasy

The sum of $x$ and $y$ is less than $15\textsf{.}$ Which inequality shows the possible values of $x$ and $y\textsf{?}$

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

Practice playmedium

At a fruit stand, apples cost $a$ dollars per pound and oranges cost $o$ dollars per pound. One customer bought $4$ pounds of apples and $2$ pounds of oranges for $\text{\char36}14\textsf{.}$ Another customer bought $2$ pounds of apples and $5$ pounds of oranges for $\text{\char36}19\textsf{.}$ What is the price of one pound of oranges?

The system is $4a + 2o = 14$ and $2a + 5o = 19\textsf{.}$ Double the second equation: $4a + 10o = 38\textsf{.}$ Subtract the first: $8o = 24\textsf{,}$ so $o = 3\textsf{.}$

Georgia Milestones Algebra I Creating Equations. Practice it free.

Creating Equations skills

Create equations that describe numbers or relationships

Create equations in two or more variables to represent relationships

Create inequalities in one variable and use them to solve problems

Topics mapped to this domain

Linear equation forms

Linear equation from two points (SAT)

Linear raise total earnings

Quadratic missing coefficient from roots (ACT)

Writing a two-variable equation from context

Compound inequality situations

Linear inequality situations (ACT/SAT/PSAT 8/9/10)

Linear system word problems (ACT/SAT)

Writing systems from context

Literal equations (SAT)

Literal quadratic equations (ACT)

Sum of consecutive integers (ACT)

8 free questions · 0/0 correct

Turn creating equations into game time.

More Algebra I domains