algebra1 EOC#7

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

Front

What does it mean for a value to be directly proportional?

Back

Two quantities are directly proportional if they increase or decrease at the same rate. This means that the ratio of the two quantities remains constant.

Front

If y is directly proportional to x, and y = 12 when x = 15, what is the constant of proportionality?

Back

The constant of proportionality (k) can be found using the formula y = kx. Here, k = y/x = 12/15 = 0.8.

Front

What is the formula for finding the total points scored in basketball?

Back

Total points = (2-point baskets × 2) + (3-point baskets × 3).

Front

How do you set up a system of equations for a word problem involving two variables?

Back

Identify the two variables, write equations based on the relationships described in the problem, and solve the system using substitution or elimination.

Front

Back

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

How can you determine the number of solutions for a system of equations?

Back

A system of equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other variable.