Linear Relationships Review

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the ratio of the change in the y-value to the change in the x-value, often represented as the slope of the line.

Tags

CCSS.HSF-LE.A.1B

Front

How do you write the equation of a line given a starting point and a rate of change?

Back

The equation can be written in the form y = mx + b, where m is the rate of change (slope) and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the steepness of the line and the direction of the relationship between the variables. A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope from a table of values?

Back

To find the slope, calculate the change in y divided by the change in x (rise/run) between two points.

Tags

CCSS.8.EE.B.5

Front

What is a y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

Given the equation y = -5x + 1, what is the slope?

Back

The slope is -5.

Tags

CCSS.8.EE.B.5

Front

If a man is descending from a height of 100 feet at a rate of 30 feet per minute, what is the equation representing his height over time?

Back

y = 100 - 30x, where y is the height and x is time in minutes.

Front

What does a negative slope indicate in a linear relationship?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Tags

CCSS.8.EE.B.5

Front

How can you determine if a table of values represents a linear relationship?

Back

If the differences between the y-values divided by the differences between the x-values are constant, the relationship is linear.

Tags

CCSS.HSF-LE.A.1B

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5