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 steep the line is and the direction it goes (positive slope means the line rises, negative slope means it falls).

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. It is represented by the value of b in the equation y = mx + b.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What does it mean if a line has an undefined slope?

Back

A line with an undefined slope is vertical, meaning it goes straight up and down. The equation of such a line is of the form x = a, where a is a constant.

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

Front

What is the significance of the equation y = mx + b?

Back

The equation y = mx + b represents a linear function where m is the slope and b is the y-intercept, providing a way to describe the relationship between x and y.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Tags

CCSS.8.EE.B.6

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Tags

CCSS.HSG.CO.A.1