Writing 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.HSF.LE.A.2

CCSS.8.F.B.4

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 find the slope of a line given 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 slope of a line that is perpendicular to another line with a slope of 3?

Back

The slope of a line that is perpendicular to another line with slope m is -1/m. Therefore, the slope of the perpendicular line is -1/3.

Tags

CCSS.8.EE.B.6

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 write the equation of a line parallel to a given line?

Back

To write the equation of a line parallel to a given line, use the same slope as the given line and substitute the coordinates of the point through which the new line passes into the point-slope form.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Tags

CCSS.8.EE.B.5

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Tags

CCSS.8.EE.B.6

Front

How can you determine if two lines are neither parallel nor perpendicular?

Back

Two lines are neither parallel nor perpendicular if they have different slopes and do not intersect at right angles.

Tags

CCSS.HSG.CO.A.1

CCSS.4.G.A.1

Front

What is a scatter plot?

Back

A scatter plot is a graph that shows the relationship between two variables by displaying data points on a two-dimensional axis.

Tags

CCSS.HSF-IF.C.7A