Mixed Review: Quadrants, Linear Equations, and Word Problems

Q1. Complete the table of values for the equation y = 5x - 24.

Background

Topic: Linear Equations and Tables

This question tests your ability to substitute values for x into a linear equation and solve for y, then organize the results in a table.

Key Terms and Formulas:

• Linear equation: $y = mx + b$

• Substitution: Replace x with a given value to solve for y.

Step-by-Step Guidance

1. Identify the values of x given in the table (e.g., x = -2, -1, 0, 1, 2).

2. For each x value, substitute it into the equation $y = 5x - 24$.

3. Calculate $y$ for each x by performing the multiplication and subtraction.

4. Record each (x, y) pair in the table.

Try solving on your own before revealing the answer!

Q2. All equations with the form x = # make a vertical line. All equations with the form y = # make a horizontal line.

Background

Topic: Graphing Linear Equations

This question is about recognizing the forms of equations that produce vertical and horizontal lines on the coordinate plane.

Key Terms and Formulas:

• Vertical line: $x = a$ (where a is a constant)

• Horizontal line: $y = b$ (where b is a constant)

Step-by-Step Guidance

1. Recall that a vertical line has an undefined slope and passes through all points with the same x-value.

2. Recall that a horizontal line has a slope of zero and passes through all points with the same y-value.

3. Identify which equations in the worksheet are in the form $x = a$ or $y = b$.

Try solving on your own before revealing the answer!

Q3. The printer charges a setup fee of $26.50 plus $0.75 for each poster printed. Write an equation for the total cost y to print x posters. Then, use the equation to find how many posters can be printed for $320.

Background

Topic: Writing and Solving Linear Equations from Word Problems

This question tests your ability to translate a real-world scenario into a linear equation and solve for an unknown variable.

Key Terms and Formulas:

• Linear equation: $y = mx + b$

• Setup fee (fixed cost): $b$

• Variable cost per item: $m$

Step-by-Step Guidance

1. Identify the fixed cost ($26.50) and the variable cost per poster ($0.75).

2. Write the equation for total cost: $y = 0.75x + 26.50$.

3. Set $y = 320$ and substitute into the equation: $320 = 0.75x + 26.50$.

4. Isolate the variable $x$ by subtracting $26.50$ from both sides.

5. Divide both sides by $0.75$ to solve for $x$.

Try solving on your own before revealing the answer!