Rearranging Formulas and Working with Linear Functions

Front

What is the rate of change of a linear function?

Back

The rate of change of a linear function is represented by the slope (m), which indicates how much the y-value changes for a unit change in the x-value.

Front

What is the formula for calculating the slope (m) between two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1)

Front

What does the slope-intercept form of a line look like?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the value of y when x = 0, represented by the point (0, b) in the slope-intercept form.

Front

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

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -2?

Back

The equation is y = 2x - 2.

Front

If a sales representative earns a commission modeled by C(x) = 4x - 10, what does the '4' represent?

Back

The '4' represents the commission earned per item sold.

Front

How do you rearrange the formula C(x) = 4x - 10 to solve for x?

Back

To solve for x, rearrange to x = (C(x) + 10) / 4.

Front

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

Back

The slope indicates the direction and steepness of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.