Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope (m) can be 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 value of y when x is 0. It is the point where the line crosses the y-axis.

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

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

Back

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

Tags

CCSS.8.EE.B.5

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting the given slope (m) and y-intercept (b).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the cost function for a plumber charging $50 for a house call and $12 per hour?

Back

The cost function is P(x) = 50 + 12x, where x is the number of hours worked.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function and simplify.

Tags

CCSS.HSF.IF.A.2

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.

Tags

CCSS.7.EE.B.4A