Slope Review

Front

What is the definition of slope in a linear equation?

Back

The slope is the ratio of the change in the y-coordinate to the change in the x-coordinate between two points on a line, often represented as 'm' in the equation y = mx + b.

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept is the value of y when x = 0. It can be found by substituting 0 for x in the equation and solving for y.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope represents the rate of change between two variables. For example, in a cost equation, it indicates how much the total cost increases for each additional hour of service.

Front

What does the y-intercept represent in a real-world scenario?

Back

The y-intercept represents the starting value of the dependent variable when the independent variable is zero.

Front

Write the equation for a line with a slope of 3 and a y-intercept of -5.

Back

The equation is y = 3x - 5.

Front

How can you determine the total cost from a rental fee structure?

Back

The total cost can be determined by adding the fixed rental fee to the variable cost, which is calculated by multiplying the hourly rate by the number of hours rented.

Front

What is the equation for a situation where a person earns a fixed amount per hour and has a debt to pay off?

Back

The equation is y = mx - b, where m is the hourly wage, and b is the total debt.

Front

How do you write an equation from a word problem involving a constant rate of change?

Back

Identify the fixed amount and the rate of change, then use the slope-intercept form to write the equation.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term (y-intercept) indicates the value of the dependent variable when the independent variable is zero.