Question

what is the slope of the line? (with a coordinate grid showing a line passing through the origin and (4,10) approximately)

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and another point, for example, when \(x = 1\), \(y = 2.5\)? Wait, no, looking at the grid, when \(x = 2\), \(y = 5\)? Wait, actually, let's take two clear points. The line goes through \((0,0)\) and \((2,5)\)? Wait, no, maybe \((1, 2.5)\) is not clear. Wait, looking at the graph, when \(x = 4\), \(y = 10\)? Wait, no, the y-axis at \(x = 4\) is 10? Wait, the grid: each square is 1 unit. So when \(x = 1\), \(y = 2.5\)? No, maybe I made a mistake. Wait, let's check the slope formula: \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: \((0,0)\) and \((2,5)\)? No, wait, when \(x = 2\), what's \(y\)? Looking at the line, at \(x = 2\), \(y = 5\)? Wait, no, the line at \(x = 1\) is at \(y = 2.5\)? No, maybe the points are \((0,0)\) and \((4,10)\). Wait, when \(x = 4\), \(y = 10\). So using \((0,0)\) and \((4,10)\):

Step2: Apply the slope formula

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 0}{4 - 0}=\frac{10}{4}=2.5\)? Wait, no, that can't be. Wait, maybe I misread the graph. Wait, the y-axis at \(x = 1\) is at \(y = 2.5\)? No, maybe the line is passing through \((0,0)\) and \((2,5)\)? Wait, no, let's check again. Wait, the grid: each square is 1 unit. So when \(x = 1\), \(y = 2.5\) is not a grid point. Wait, maybe the points are \((0,0)\) and \((1, 2.5)\) no, that's not helpful. Wait, maybe the line is \(y = 2.5x\), but that's not an integer. Wait, maybe I made a mistake. Wait, let's look at the graph again. The line starts at (0,0) and goes up to (4,10)? Wait, no, the y-axis at x=4 is 10? Wait, the y-axis is labeled from 0 to 10, and x from 0 to 10. So at x=4, y=10. So slope is (10-0)/(4-0)=10/4=2.5? But that's 5/2. Wait, maybe the points are (0,0) and (2,5). Then slope is (5-0)/(2-0)=5/2=2.5. Alternatively, (0,0) and (1, 2.5), but that's the same. Wait, maybe the correct points are (0,0) and (2,5), so slope is 5/2=2.5. Wait, but maybe the line is passing through (0,0) and (1, 2.5), but that's not a grid point. Wait, maybe the line is \(y = 2.5x\), so slope is 2.5, which is 5/2. But maybe I misread the graph. Wait, let's check again. The line at x=1 is at y=2.5, x=2 at y=5, x=3 at y=7.5, x=4 at y=10. So yes, the slope is 10/4=2.5, which is 5/2. Wait, but maybe the problem is designed with integer slope. Wait, maybe I made a mistake. Wait, maybe the points are (0,0) and (2,5), so slope is 5/2=2.5. Alternatively, maybe the line is y=2.5x, so slope is 2.5.

Wait, maybe I should take (0,0) and (1, 2.5), but that's the same. Alternatively, maybe the graph is scaled differently. Wait, the y-axis at x=1 is at y=2.5, which is 5/2. So the slope is 5/2 or 2.5.

But let's check again. The line passes through (0,0) and (4,10). So slope is (10-0)/(4-0)=10/4=5/2=2.5. So the slope is 5/2 or 2.5.

Answer:

The slope of the line is \(\frac{5}{2}\) (or 2.5).