Linear Equations in the Real World

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 value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

The equation can be written in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the cost equation for renting a moped from Scoots Inc.?

Back

y = 0.50x + 20, where y is the total cost and x is the number of miles driven.

Front

In the equation y = 0.50x + 20, what does the 20 represent?

Back

The 20 represents the one-time rental fee for the moped.

Front

If Jacob delivers pizzas and earns $3 per pizza, how can we express his total earnings?

Back

His total earnings can be expressed as y = 3x + 25, where y is total money made and x is the number of pizzas delivered.

Front

What is the equation representing Ms. Deppe's savings after x months?

Back

y = 40x + 150, where y is the total amount in her savings account after x months.

Front

How do you determine the x and y variables in a real-world scenario involving linear equations?

Back

The x variable typically represents the independent variable (like time or quantity), while the y variable represents the dependent variable (like total cost or earnings).

Front

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

Back

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