Proportional Functions 7.10a,b

Front

What is a proportional function?

Back

A proportional function is a linear function that passes through the origin (0,0) and can be expressed in the form y = kx, where k is the constant of proportionality.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (-1, -3) and (3, 1)?

Back

The slope is m = (1 - (-3)) / (3 - (-1)) = 4/4 = 1.

Front

What is the equation of a line with a slope of 3 that passes through the point (-1, -3)?

Back

The equation is y = 3x + 0, or y = 3x.

Front

If a dog has 4 paws, what is the slope of the relationship between the number of dogs and the number of paws?

Back

The slope is m = 4, since each dog contributes 4 paws.

Front

What does it mean if a function is linear?

Back

A linear function is a function that graphs to a straight line, meaning it has a constant rate of change.

Front

What is the y-intercept in the equation y = 19.25x?

Back

The y-intercept is 0, as the line passes through the origin.

Front

How can you express the relationship between hours worked and money earned if you earn $7.50 per hour?

Back

The relationship can be expressed as y = 7.50x, where y is the total earnings and x is the number of hours worked.

Front

What is the constant of proportionality in the equation y = 19.25x?

Back

The constant of proportionality is 19.25.