Practice Test on Writing Linear Equations and Problem Solving

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form Ax + By = C, where A, B, and C are constants.

Front

What does the slope-intercept form of a linear equation look like?

Back

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

If a plumber charges $50 for a house call and $25 per hour, how would you express the total cost as a linear equation?

Back

The total cost (y) can be expressed as y = 25x + 50, where x is the number of hours worked.

Front

How do you solve for x in the equation 2x + 3 = 11?

Back

To solve for x, subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4.

Front

What is the total cost for 2.5 hours of labor if the hourly rate is $25?

Back

The total cost is $25 * 2.5 = $62.50, plus the $50 house call fee, totaling $112.50.

Front

How do you write an equation for a situation with a fixed fee and a variable cost?

Back

You can write the equation in the form y = mx + b, where m is the variable cost per unit and b is the fixed fee.

Front

If a moving truck costs $0.50 per mile and the total cost for 48 miles is $64, how do you find the daily fee?

Back

Let y be the total cost, x be the miles driven. The equation is y = 0.50x + b. Substitute y = 64 and x = 48 to find b.

Front

What is the equation for the cost of joining a dancing club with a startup fee and monthly fee?

Back

The equation is y = 4x + 30, where y is the total cost and x is the number of months.