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.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the y-intercept?

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

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

Write the equation of a line with a slope of 3 and a y-intercept of 4.

Back

The equation is y = 3x + 4.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

The slope of the line is -2.

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Tags

CCSS.8.EE.B.5

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line that is vertical?

Back

The equation of a vertical line is of the form x = a, where 'a' is the x-coordinate of any point on the line.

Front

How do you write an equation from a word problem involving a constant rate?

Back

Identify the constant rate as the slope and the starting value as the y-intercept, then use the form y = mx + b.