Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = 3/2x + 3?

Back

The slope of the line is 3/2.

Front

What is the y-intercept of the line represented by the equation y = 3/2x + 3?

Back

The y-intercept is the point (0, 3).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the formula for 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 can you determine the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (-2, 1) and (5, 7)?

Back

The slope is 6/7.

Front

Which equation represents a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.