EM7 - Writing Equations from Scenarios

Front

What is the general form of a linear equation representing a relationship between two variables?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you represent a situation where a quantity increases by a constant amount over time?

Back

You can represent this situation with a linear equation of the form y = mx + b, where m is the constant rate of increase.

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).

Front

In the equation y = 15x + 80, what do the numbers 15 and 80 represent?

Back

In this equation, 15 represents the rate of increase in membership per month (slope), and 80 represents the initial number of members (y-intercept).

Front

How can you express the area of a rectangle if the length is increased by a certain amount?

Back

If the length is increased by a certain amount, the new area can be expressed as A = (l + increase) * w.

Front

What is the formula for calculating the total cost when there is a fixed fee and a variable cost per unit?

Back

The total cost can be calculated using the formula C = fixed fee + (variable cost per unit * number of units).

Front

In the context of a cell phone bill, what does the fixed fee represent?

Back

The fixed fee represents the base charge that is incurred regardless of usage.

Front

How do you write an equation for a situation involving a deposit and a variable cost?

Back

You write the equation as C = variable cost * number of units + deposit fee.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero; it represents the starting point of the relationship.

Front

How can you determine the total height of a plant growing at a constant rate?

Back

You can determine the total height using the equation y = growth rate * time + initial height.