Proportional Relationships Flashcard

Front

This graph shows a proportional relationship between the number of pages Sally reads and the time she takes in minutes. Which statement identifies the correct slope and the correct interpretation of the slope for this situation? Options: The slope of the line is 1/2, so Sally reads 0.5 of a page every minute. The slope of the line is 1/2, so Sally reads 2 pages every minute. The slope of the line is 2/1, so Sally reads 0.5 of a page every minute. The slope of the line is 2/1, so Sally reads 2 pages every minute.

Back

The slope of the line is 1/2, so Sally reads 0.5 of a page every minute.

Answer explanation

The slope of 1/2 indicates that for every minute, Sally reads 0.5 pages. This means she reads half a page each minute, confirming the correct choice.

Front

Line t has slope 3/4 and passes through (0, 0). Start at (0, 0), move right 8 units. How many units up is line t?

Back

6

Answer explanation

The slope of line t is 3/4. Moving right 8 units means we increase x by 8. The corresponding increase in y is (3/4) * 8 = 6. Thus, from (8, 0), line t is 6 units up.

Front

Equation of the line in the form y = mx where m is the slope.

Back

y=3x

Answer explanation

The equation of a line in the form y = mx indicates that m is the slope. The correct answer is y = 3x, where the slope m is 3.

Front

Equation of the line in the form y = mx + b where m is the slope and b is the y-intercept.

Back

y = 3x - 2

Answer explanation

The equation y=3x-2 is in the form y=mx+b, where m (slope) is 3 and b (y-intercept) is -2. This matches the required format, confirming it as the correct answer.

Front

Equation showing a distance per hour that is 2 times more than the distance Paul covered per hour.

Back

d = 8h

Answer explanation

To find the equation showing a distance per hour that is 2 times more than Paul's distance per hour, we need to double the coefficient of h. If Paul covers 4h, then 2 times that is 8h, making d = 8h the correct choice.

Front

Equation of the line in the form y = mx + b

Back

y = 3/2x - 2

Answer explanation

The equation y=3/2x-2 is in the form y=mx+b, where m (slope) is 3/2 and b (y-intercept) is -2. This matches the required format, confirming it as the correct answer.

Front

Equation representing the relationship between cookies sold (c) and profit earned (p).

Back

p=1/2c

Answer explanation

The equation p=1/2c suggests that for every 2 cookies sold, the profit is 1 unit. However, the question asks for an equation that represents the relationship, and since no specific equation is provided, the correct answer is 0.

Front

Triangle ABC is given with coordinates A(−7, −4), B(−7, 4), and C(1, 4). The ordered pair (6, y) is on line AC. Enter the value of y for this ordered pair.

Back

y=9

Answer explanation

To find the value of y for the point (6, y) on line AC, we first determine the equation of line AC using points A(−7, −4) and C(1, 4). The slope is (4 - (-4)) / (1 - (-7)) = 1. The line equation is y = x + 3. Substituting x = 6 gives y = 6 + 3 = 9.