Interpreting Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

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 y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, set x to 0 and solve for y. The value of y will be the y-intercept.

Front

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

Back

The equation is y = 2x + 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

If a linear function has a slope of -1, what does this indicate about the function?

Back

A slope of -1 indicates that for every unit increase in x, y decreases by 1 unit, showing a negative relationship.

Tags

CCSS.8.EE.B.5

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Tags

CCSS.HSF-LE.A.1B

Front

What does the term 'rate of change' mean in the context of linear functions?

Back

Rate of change refers to how much the output (y) changes for a given change in the input (x). In linear functions, this is constant and equal to the slope.

Tags

CCSS.HSF-LE.A.1B

Front

How do you write the equation of a line given two points (x1, y1) and (x2, y2)?

Back

First, calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

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

Back

The x-intercept is the value of x when y is 0. It is the point where the line crosses the x-axis.