Question

1. how would you describe the slope in the picture? a) positive b) zero c) negative d) undefined 9. how would you describe the slope in the picture? a) undefined b) zero c) negative d) positive

Explanation:

Question 8

To determine the slope, we analyze the direction of the line (or surface) in the picture. A positive slope rises from left to right, a negative slope falls from left to right, zero slope is horizontal, and undefined is vertical. The snow slope in the picture appears to fall from left to right (as the skier moves down, the height decreases as we move from left to right), so the slope is negative? Wait, no—wait, maybe I got it reversed. Wait, actually, when moving from left to right, if the line goes up, it's positive; down, negative. Wait, the skier is going down a slope that, from left to right, is decreasing in height? Wait, no, maybe the slope is negative? Wait, no, let's think again. Wait, the slope formula is \( \text{slope} = \frac{\text{change in } y}{\text{change in } x} \). If we take two points on the slope, say left and right, as \( x \) increases (moves right), \( y \) (height) decreases. So \( \frac{\Delta y}{\Delta x} \) is negative? Wait, no, maybe I made a mistake. Wait, the skier is going down a slope that, from left to right, is going down, so the slope is negative? Wait, no, actually, the slope of a downhill (from left to right) is negative? Wait, no, let's check the options. Wait, the options are positive, zero, negative, undefined. Wait, maybe the slope is negative? Wait, no, maybe I got it wrong. Wait, the snow slope: if you imagine a coordinate system where the bottom left is (0,0) and moving right is positive x, up is positive y. The slope of the snow surface: as x increases, y decreases, so slope is negative? Wait, but maybe the answer is c) Negative? Wait, no, wait, maybe the slope is negative. Wait, but let's re-express. Wait, the skier is going down a slope that is slanting downward from left to right, so the slope is negative. So the answer for question 8 is c) Negative? Wait, no, wait, maybe I made a mistake. Wait, no, let's think again. Wait, the slope of a line that goes down from left to right is negative. So the snow slope in question 8: as you move from left to right, the height decreases, so slope is negative. So question 8 answer is c) Negative.

Question 9

For the car on the slope: as we move from left to right (increasing x), the height (y) increases (the car is going up the slope from left to right). So the slope is positive because \( \frac{\Delta y}{\Delta x} \) is positive (since \( \Delta y \) and \( \Delta x \) are both positive). So the slope is positive, so the answer is d) Positive.

Answer:

s:

1. c) Negative
2. d) Positive