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

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y (vertical) divided by the change in x (horizontal). It is often represented as 'm' in the slope-intercept form of a linear equation, y = mx + b.

Front

How do you calculate the slope from 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 a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

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 the constant of variation.

Front

If y varies directly as x and k = 3, what is the equation?

Back

The equation is y = 3x.

Front

How do you find the constant of variation (k) in direct variation?

Back

To find k, use the formula k = y/x, where y is the output and x is the input.

Front

If a car travels 280 miles in 7 hours, what is its speed in miles per hour?

Back

The speed is 40 miles per hour, calculated as 280 miles / 7 hours.

Front

If y = 10 when x = 2 in a direct variation, what is the constant of variation (k)?

Back

The constant of variation (k) is 5, calculated as k = y/x = 10/2.

Front

What is the slope of the line represented by the points (1, 2) and (3, 6)?

Back

The slope is 2, calculated as m = (6 - 2) / (3 - 1) = 4/2 = 2.