Slope and Proportional Relationships Review

Front

What is the definition of slope in a linear relationship?

Back

Slope is a measure of the steepness of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise/run).

Front

What does a proportional relationship mean?

Back

A proportional relationship is one in which two quantities maintain a constant ratio, meaning that as one quantity increases, the other quantity increases at a consistent rate.

Front

How do you find the unit rate from a given total cost and quantity?

Back

To find the unit rate, divide the total cost by the quantity. For example, if $3.60 is for 3 pounds of apples, the unit rate is $3.60 ÷ 3 = $1.20 per pound.

Front

What is the significance of the origin in determining proportional relationships?

Back

A proportional relationship must pass through the origin (0,0). If it does not, it is considered non-proportional.

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of 3, what does this indicate about the relationship between x and y?

Back

A slope of 3 indicates that for every 1 unit increase in x, y increases by 3 units.

Front

What does it mean if a graph intersects the y-axis?

Back

If a graph intersects the y-axis, it indicates the y-intercept, which is the value of y when x is 0.

Front

How can you determine if a relationship is linear?

Back

A relationship is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

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

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.