Slope Final

Mugdha and Dhruvi are on a treasure hunt and need to find the slope of the path that leads them from point A (5, 8) to point B (−4, 6). Can you help them calculate the slope of the line passing through these points?

• The slope of the line passing through the points (5, 8) and (−4, 6) is calculated using the formula: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (5, 8) and (x2, y2) = (−4, 6). Thus, slope = (6 - 8) / (−4 - 5) = -2 / -9 = 2/9.

• The slope of the line passing through the points (5, 8) and (−4, 6) is calculated using the formula: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (5, 8) and (x2, y2) = (−4, 6). Thus, slope = (8 - 6) / (5 - (-4)) = 2 / 9.

• The slope of the line passing through the points (5, 8) and (−4, 6) is calculated using the formula: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (5, 8) and (x2, y2) = (−4, 6). Thus, slope = (6 - 8) / (5 - (-4)) = -2 / 9.

• The slope of the line passing through the points (5, 8) and (−4, 6) is calculated using the formula: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (5, 8) and (x2, y2) = (−4, 6). Thus, slope = (8 - 6) / (-4 - 5) = 2 / -9.

Answer explanation

The correct slope is calculated as (y2 - y1) / (x2 - x1). Using (5, 8) and (−4, 6), we find slope = (6 - 8) / (−4 - 5) = -2 / -9 = 2/9, matching the first answer choice.

Aahana and Anshika are on a treasure hunt! They need to find the slope of the path that leads from the mysterious point (9, 4) to the hidden treasure at (5, −3). Can you help them calculate the slope of their adventurous journey?

• The slope of the line passing through the points (9, 4) and (5, −3) is calculated using the formula: slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (9, 4) and (x2, y2) = (5, -3). Therefore, slope = (-3 - 4) / (5 - 9) = -7 / -4 = 7/4.

• The slope of the line passing through the points (9, 4) and (5, −3) is 4/7.

• The slope of the line passing through the points (9, 4) and (5, −3) is -7/4.

• The slope of the line passing through the points (9, 4) and (5, −3) is 0.

Answer explanation

To find the slope between (9, 4) and (5, -3), use slope = (y2 - y1) / (x2 - x1). Here, slope = (-3 - 4) / (5 - 9) = -7 / -4 = 7/4. Thus, the correct answer is 7/4.

Imagine Jude and Aahana are climbing a mountain, and they want to calculate the slope of their path. Why can't they use the Slope Formula if their path is a vertical line?

• Because the slope is undefined for vertical lines.

• Because vertical lines have a slope of zero.

• Because vertical lines have a positive slope.

• Because vertical lines have a negative slope.

Answer explanation

The correct choice is that the slope is undefined for vertical lines. This is because vertical lines do not have a change in x-coordinates, leading to division by zero when calculating slope.

Jude and Ani are on a treasure hunt! They found a mysterious map with a line drawn on it. Can you help them find the slope of the line?

• 3/2

• -3/2

• (-0,-3)

• none of the above

Answer explanation

To find the slope, use the formula (change in y) / (change in x). Given the slope is 3/2, this indicates that for every 2 units moved horizontally, the line rises 3 units vertically. Thus, the correct answer is 3/2.

Adriana and Ashley are on a treasure hunt! They need to find the slope of the mysterious path that passes through the points (2, 3) and (6, 7) to unlock the next clue. Can you help them calculate it?

• 1

• 2

• 1/2

• 4

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (7 - 3) / (6 - 2) = 4 / 4 = 1. Thus, the slope of the line is 1.

Ashley and Milana are on a treasure hunt! They need to find the slope of the path that leads from the mysterious point (−2, −1) to the hidden treasure at (4, 3). Can you help them determine the slope of their adventurous journey?

• 3/2

• 1

• 2/3

• 4/3

Answer explanation

To find the slope (m) between points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (3 - (-1)) / (4 - (-2)) = 4 / 6 = 2/3. The correct slope is 3/2.

Adriana and Ani are on a treasure hunt and need to find the slope of the path that leads them from the mysterious point (−3, −2) to the hidden treasure at (3, 4). Can you help them calculate the slope of their adventurous journey?

• 1

• 2

• 3

• 4

Answer explanation

To find the slope (m) between two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1). Here, m = (4 - (-2)) / (3 - (-3)) = 6 / 6 = 1. Thus, the slope is 2.

Milana and Jovany are on a treasure hunt! They start at the point (0, 5) and move to the point (5, 5) on their map. Can you help them find the slope of the path they took?

• 0

• 1

• 2

• undefined

Answer explanation

The slope of a line is calculated as (y2 - y1) / (x2 - x1). For points (0, 5) and (5, 5), the slope is (5 - 5) / (5 - 0) = 0 / 5 = 0. Thus, the correct answer is 0.

In 2005, Aryaa and Mohammed were part of the 12,000 students at Beacon High. By 2010, Anshika joined them, and the student count rose to 12,250. Can you calculate the magical rate of change in the number of students over these years?

• 250/yr

• 50/yr

• 42/yr

• 200/yr

Answer explanation

To find the rate of change, subtract the initial number of students (12,000) from the final number (12,250) to get 250. Then, divide by the number of years (5). Thus, 250/5 = 50 students per year.

Find the slope:

Mathematical Equivalence

ON