Flashcard 3.4 Review (Slope from a Table & Graph; Direct Variation)

Front

What is the formula for calculating the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a slope of 0 indicate about a line on a graph?

Back

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

Front

What does a positive slope indicate about the relationship between x and y?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

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

Back

To determine the slope from a table, calculate the change in y divided by the change in x (Δy/Δx) between two points.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

If y varies directly with x and y = 20 when x = 4, what is the constant of variation (k)?

Back

The constant of variation (k) is found by rearranging the equation: k = y/x. Here, k = 20/4 = 5.

Front

How do you find the value of y when x is given in a direct variation problem?

Back

To find y, use the formula y = kx, where k is the constant of variation.

Front

If the cost of producing x units is directly proportional to x, what is the cost of producing 10 units if 5 units cost $25?

Back

First, find the constant of variation: k = 25/5 = 5. Then, for 10 units, cost = k * 10 = 5 * 10 = $50.

Front

What is the relationship between the slope of a line and direct variation?

Back

In direct variation, the slope of the line representing the relationship is equal to the constant of variation (k).