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 the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

How do you calculate the slope from 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 in a linear function?

Back

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

Front

If a linear function has a slope of 4, what does this mean?

Back

A slope of 4 means that for every 1 unit increase in x, the value of y increases by 4 units.

Tags

CCSS.HSF.LE.B.5

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation 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

How do you find the cost function for a service with a fixed fee and a variable rate?

Back

The cost function can be expressed as C(x) = fixed fee + (variable rate * x), where x is the number of units (e.g., hours of service).

Tags

CCSS.HSF.LE.B.5

Front

What is the equation of a line with a slope of 3 and a y-intercept of 6?

Back

The equation of the line is y = 3x + 6.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does a linear graph look like?

Back

A linear graph is a straight line that can either be increasing, decreasing, or constant.

Front

How can you determine if a graph is linear?

Back

A graph is linear if it forms a straight line when plotted on a coordinate plane.

Tags

CCSS.8.F.A.3