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 point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you convert a word problem into a linear equation?

Back

Identify the variables, determine the relationship between them, and translate the words into mathematical expressions using operations like addition, subtraction, multiplication, and division.

Front

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

Back

C = 8m + 50

Front

If Evan spends $10 to enter a fair and $2 per ride, how would you express the total cost (y) for x rides?

Back

y = 2x + 10

Front

What is the equation that models Dexter's Gym's total fee after x months if there is a $40 registration fee and $20 monthly fee?

Back

20x + 40 = total fee

Front

In the equation y = mx + b, what does 'x' represent?

Back

'x' represents the independent variable, which is the input value for the function.

Front

In the equation y = mx + b, what does 'y' represent?

Back

'y' represents the dependent variable, which is the output value that depends on the value of 'x'.

Front

What is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation by using inverse operations.