Linear Equations Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line when graphed. It can be expressed 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 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 is the value of y when x is 0. It represents the starting point of the linear relationship on the y-axis.

Front

How can you interpret the y-intercept in a real-world context?

Back

In a real-world context, the y-intercept often represents a fixed cost or initial amount before any variable costs are added.

Front

What is the general form of a linear equation representing a total cost?

Back

The general form is y = mx + b, where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

How do you set up a linear equation from a word problem?

Back

Identify the variables, determine the fixed and variable costs, and express the relationship between the total amount and the variables in the form of a linear equation.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients indicate the relationship between the variables. The coefficient of x (slope) shows the rate of change, while the constant term (y-intercept) shows the initial value.

Front

How can you find the total cost if you know the number of items purchased?

Back

Substitute the number of items into the linear equation and solve for y to find the total cost.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

How do you interpret the equation y = mx + b in a real-world scenario?

Back

In a real-world scenario, y represents the total outcome (like cost), m represents the rate of change (like cost per item), x represents the quantity, and b represents any fixed starting value.