Question

Question was provided via image upload.

Explanation:

Step1: Determine vertical change

From the starting point (where the left arrow is) to a point on the line, count the vertical units. Moving up, let's say we move 3 units (as a sample, but visually, let's check the grid). Wait, actually, looking at the line, for a run (right) of, say, 6, the rise (up) is also 6? Wait, no, let's take two points. Let's pick a point on the line, say when x increases by 6, y increases by 3? Wait, no, maybe I misread. Wait, the grid: let's see the line. Let's take the starting point (the left arrow) and then move right. Wait, maybe the vertical change (up/down) and horizontal change (right). Let's count the squares. Suppose from the starting point (the left - pointing arrow's position) to a point on the line, moving up: let's say 3 units? Wait, no, maybe the slope is rise over run. Let's take two points. Let's say the line passes through (0,0) and (6,3)? No, wait, maybe the correct way: look at the grid. Let's take the starting point (the left arrow) and then move right. Let's count the vertical change (up) and horizontal change (right). Let's say when we move right 6 units, we move up 3 units? No, wait, maybe the slope is 3/6 = 1/2? Wait, no, let's do it properly. Let's pick two points on the line. Let's say the line goes through ( - 6,0) and (0,3)? No, maybe better to count the rise and run. Let's take the starting point (the left arrow) and then move to a point on the line. Let's count the vertical (up/down) and horizontal (right) distances. Let's say we move up 3 units (vertical) and right 6 units (horizontal). Then slope = rise/run = 3/6 = 1/2? Wait, no, maybe I made a mistake. Wait, the first example had slope 1 (3/3). Now, for the second line, let's count the rise and run. Let's take two points: suppose the line passes through ( - 4, - 2) and (4,2)? No, maybe the grid is 1 - unit per square. Let's look at the line: from the left - most point (where the left arrow is) to a point on the line, moving right 6 units, moving up 3 units? Wait, no, let's check the slope formula. Slope = (y2 - y1)/(x2 - x1). Let's pick two points on the line. Let's say the line goes through ( - 6,0) and (0,3). Then y2 - y1 = 3 - 0 = 3, x2 - x1 = 0 - ( - 6)=6. So slope = 3/6 = 1/2. Wait, but maybe the vertical change (up/down) is 3 and horizontal change (right) is 6? Wait, no, maybe I messed up. Wait, the first example had slope 1 (3/3). Now, for the second line, let's count the rise and run. Let's take the starting point (the left arrow) and then move right. Let's count the number of squares up (vertical) and right (horizontal). Let's say we move up 3 units (vertical) and right 6 units (horizontal). Then slope = 3/6 = 1/2. Wait, but maybe the correct numbers: let's look at the grid. Let's say the vertical change (up) is 3 and horizontal change (right) is 6. Then slope = 3/6 = 1/2.

Step2: Calculate slope

Slope is rise over run, so slope = (up/down) / (right). If up/down is 3 and right is 6, then slope = 3/6 = 1/2. Wait, maybe the vertical change is 3 and horizontal change is 6. So up/down: 3, right: 6, slope = 3/6 = 1/2.

Answer:

Up/down: 3, Right: 6, slope = $\frac{1}{2}$ (Note: The values may vary slightly depending on the exact points chosen, but the key is slope = rise/run. If we take other points, for example, up 2 and right 4, slope is also 1/2. But based on the grid, a reasonable count is up 3, right 6, slope 1/2)