Write Linear Equations from 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 point where the line crosses the y-axis. It is the value of y when x is 0.

Front

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

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

If a man descends 30 feet per minute from a height of 100 feet, what is the linear equation representing his height over time?

Back

y = -30x + 100, where y is the height and x is the time in minutes.

Front

Sandra has a $20 iTunes gift card and spends $3 each month. Write the equation for her remaining balance after x months.

Back

y = -3x + 20, where y is the remaining balance and x is the number of months.

Front

Connor sells lemonade, starting with 15 cups and selling 5 more each hour. Write the equation for the total cups sold after x hours.

Back

y = 5x + 15, where y is the total cups sold and x is the number of hours.

Front

What does the equation y = 1/4 x + 2 represent?

Back

This equation represents a line with a slope of 1/4 and a y-intercept of 2.

Front

How can you determine which linear equation matches a given graph?

Back

By analyzing the slope and y-intercept of the graph and comparing them to the equations provided.

Front

What is the significance of the negative slope in the equation y = -x + 2?

Back

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