Writing Linear Equations in Context

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 of a linear equation represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable. It indicates how much y changes for a unit change in x.

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How do you write an equation for a cost function based on a base cost and variable cost per item?

Back

The equation can be written as C = base cost + (variable cost per item * number of items).

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 function on the y-axis.

Front

How can you determine the cost of a pizza with toppings using a linear equation?

Back

You can write the equation as C = base cost + (cost per topping * number of toppings). For example, if the base cost is $11.99 and each topping costs $1.25, the equation is C = 11.99 + 1.25t.

Front

What is the formula to calculate remaining gasoline in a tank over time?

Back

The formula is G = initial amount - (rate of consumption * time). For example, if the initial amount is 19 gallons and the rate is 3 gallons per hour, the equation is G = 19 - 3t.

Front

What does the term 'per-mile fee' mean in the context of renting a truck?

Back

The per-mile fee is the additional cost charged for each mile driven with the rented truck, represented as the slope in the equation y = mx + b.

Front

How do you model tuition increases over time with a linear equation?

Back

You can model tuition increases with the equation T = initial tuition + (increase per year * number of years). For example, T = 10,250 + 500t.

Front

What is the significance of the initial cost in a linear earnings equation?

Back

The initial cost represents the fixed expenses that must be covered before any profit is made, often referred to as the y-intercept in the earnings equation.

Front

How do you express earnings based on the number of services provided?

Back

The earnings can be expressed as m = (earnings per service * number of services) - initial costs. For example, m = 60L - 395.