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 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 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 value of y when x = 0 is the y-intercept.

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 determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope (m) is negative.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation of the line is y = 2x - 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

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 m is the slope and (x1, y1) is a point on the line.

Front

If a line passes through the points (1, 2) and (3, 6), what is its slope?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of the equation y = -4x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3