Slope: Review

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean for a relationship to be proportional?

Back

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

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

If a washing machine uses 28 gallons for 7 pounds of laundry, what is the constant of variation?

Back

The constant of variation (k) is 4 gallons per pound, calculated as k = 28 gallons / 7 pounds.

Front

How do you determine if a table of values represents a proportional relationship?

Back

A table represents a proportional relationship if the ratios of corresponding values are constant.

Front

What is the slope of a line that decreases from left to right?

Back

The slope of a line that decreases from left to right is negative.

Front

What is the slope of a line that increases from left to right?

Back

The slope of a line that increases from left to right is positive.

Front

How can you identify a non-proportional relationship from a graph?

Back

A non-proportional relationship can be identified from a graph if the line does not pass through the origin (0,0) or if the line is not straight.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.