Intercepts of Linear Functions (with context)

Front

What is the domain of a linear function?

Back

The domain of a linear function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a linear function?

Back

The range of a linear function is the set of all possible output values (y-values) that the function can produce.

Front

What does the x-intercept represent in a linear function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, indicating the value of x when y = 0.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of y when x = 0.

Front

How do you find the x-intercept of the equation 3x + 8y = 24?

Back

To find the x-intercept, set y = 0 and solve for x. The x-intercept is (8, 0).

Front

How do you find the y-intercept of the equation 3x + 8y = 24?

Back

To find the y-intercept, set x = 0 and solve for y. The y-intercept is (0, 3).

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

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it shows how much y changes for a unit change in x.

Front

How can you interpret the equation 15x + 20y = 150 in context?

Back

This equation represents a relationship between the number of T-shirts (x) and hoodies (y) Jenny can buy, given her budget.

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.