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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive, negative, zero, or undefined).

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

Tags

CCSS.8.EE.B.5

Front

What is the significance of a zero slope?

Back

A zero slope indicates a horizontal line, meaning that y remains constant regardless of the value of x.

Tags

CCSS.8.EE.B.5

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant and y can take any value.

Tags

CCSS.8.EE.B.5