Linear Equations Word Problems

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you write an equation in slope-intercept form?

Back

To write an equation in slope-intercept form, identify the slope (m) and the y-intercept (b) from the context of the problem and use the format y = mx + b.

Front

What is the equation for the total cost of towing a vehicle if the flat fee is $50 and the cost per mile is $8?

Back

C = 8m + 50, where C is the total cost and m is the number of miles.

Front

If a gym membership costs $50 per month and a one-time fee, how do you find the membership fee if the total bill is $221 for four months?

Back

Let the membership fee be x. The equation is 4(50) + x = 221. Solving gives x = $21.

Front

How can you represent the relationship between the number of people on a bus and the cost charged by a ferry?

Back

You can use the equation y = 2x + 120, where y is the cost and x is the number of people.

Front

What is the equation for Alex's weight loss if he loses 2 pounds per week and weighs 205 pounds after 6 weeks?

Back

The equation is y = -2x + 217, where y is his weight and x is the number of weeks.

Front

What is the first step in solving a linear equation word problem?

Back

Identify the variables involved and what they represent in the context of the problem.

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.