Linear equation word problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 in a linear equation represent?

Back

The slope (m) in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) in a linear equation is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you write an equation for a word problem involving savings?

Back

To write an equation for a savings problem, identify the initial amount and the rate of saving. The equation will typically be in the form y = mx + b, where m is the monthly savings and b is the initial amount.

Front

What is the equation for the total cost of an item with a setup fee and a per-item cost?

Back

The equation for total cost can be written as y = mx + b, where m is the cost per item, x is the number of items, and b is the setup fee.

Front

How do you determine the total cost after a certain number of months in a membership scenario?

Back

To determine the total cost after a certain number of months, use the equation y = mx + b, where m is the monthly fee, x is the number of months, and b is the initial fee.

Front

What is the significance of the initial value in a linear equation?

Back

The initial value in a linear equation represents the starting point of the situation being modeled, such as the initial amount of money or the starting number of members.

Front

How can you find the number of months until a total cost reaches a specific amount?

Back

To find the number of months until a total cost reaches a specific amount, rearrange the equation to solve for x: x = (y - b) / m, where y is the total cost, b is the initial fee, and m is the monthly fee.

Front

What is the formula to calculate the total cost of towing a vehicle based on miles towed?

Back

The total cost of towing can be calculated using the equation C = 8m + 50, where C is the total cost, m is the number of miles, 8 is the cost per mile, and 50 is the flat fee.

Front

How do you interpret the coefficients in a linear equation?

Back

The coefficients in a linear equation indicate the relationship between the variables. The slope shows the rate of change, while the y-intercept shows the starting value.