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 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 steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you calculate the total cost from a linear equation?

Back

To calculate the total cost, substitute the number of items (x) into the equation and solve for y.

Front

If a shirt costs $8 and there is a $15 setup fee, what is the equation for total cost?

Back

The equation is y = 8x + 15, where y is the total cost and x is the number of shirts.

Front

How do you interpret the equation y = -25x + 120?

Back

This equation represents a situation where the value decreases by 25 for each unit increase in x, starting from 120.

Front

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

Back

Coefficients indicate the relationship between variables; they show how much y changes for a unit change in x.

Front

How can you find the number of items you can buy with a budget using a linear equation?

Back

Set up the equation based on the cost per item and total budget, then solve for the number of items.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express it in the form y = mx + b.