Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form f(x) = 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 y-value with respect to the x-value. 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

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

Front

What is the x-intercept of a line?

Back

The x-intercept of a line is the point where the line crosses the x-axis. To find it, set y = 0 in the equation and solve for x.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept indicates the value of the function when x = 0. It is the starting point of the line on the y-axis.

Tags

CCSS.HSF-IF.C.7A

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function f(x) at a specific point x = a, substitute a into the function and simplify to find f(a).

Tags

CCSS.HSF.IF.A.2

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They 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. This means one line has a slope that is the negative reciprocal of the other.

Tags

CCSS.8.EE.B.6