Real-World Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models 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 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 line on the y-axis.

Front

How do you write an equation in slope-intercept form?

Back

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

Front

What is the significance of the initial fee in a real-world linear equation?

Back

The initial fee represents a fixed cost that does not change with the number of units (e.g., months, children) and is often the y-intercept in the equation.

Front

How can you determine the total cost after a certain number of months using a linear equation?

Back

You can substitute the number of months into the equation to find the total cost. For example, if the equation is y = 20x + 40, and x = 5, then y = 20(5) + 40 = 140.

Front

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

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases. This shows an inverse relationship.

Front

How do you interpret the slope in a real-world context?

Back

The slope can be interpreted as the rate of change. For example, if the slope is 15 in a membership equation, it means the membership increases by 15 members each month.

Front

What is the formula to find the total cost when there is a fixed fee and a variable cost?

Back

The formula 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 fee.

Front

How do you find the equation of a line given two points?

Back

To find the equation, first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Then use one of the points to solve for b in the equation y = mx + b.