Question

find the slope of each line shown on the graph to the right.
the slope of the line ( l_1 ) is \\( \square \\).

Explanation:

Step1: Identify two points on \( L_1 \)

From the graph, we can see that \( L_1 \) passes through the points \((-10, -5)\) and \((10, 7)\) (or other clear points, let's verify with \((0, 2)\) and \((10, 7)\) for simplicity: when \( x = 0 \), \( y = 2 \); when \( x = 10 \), \( y = 7 \)). Wait, better to take two clear grid points. Let's take \((-10, -5)\) and \((10, 7)\)? Wait, no, looking at the blue line \( L_1 \), when \( x = -10 \), \( y = -5 \); when \( x = 0 \), \( y = 2 \). Let's use \((-10, -5)\) and \((0, 2)\).

Step2: Use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Let \((x_1, y_1) = (-10, -5)\) and \((x_2, y_2) = (0, 2)\). Then \( m = \frac{2 - (-5)}{0 - (-10)} = \frac{2 + 5}{0 + 10} = \frac{7}{10} \)? Wait, no, maybe better points. Wait, when \( x = 0 \), \( y = 2 \); when \( x = 10 \), \( y = 7 \). So \( (0, 2) \) and \( (10, 7) \). Then slope \( m = \frac{7 - 2}{10 - 0} = \frac{5}{10} = \frac{1}{2} \). Wait, let's check another pair: \( (-10, -3) \)? Wait, maybe I misread. Wait, the blue line \( L_1 \): when \( x = -10 \), \( y = -5 \)? No, looking at the grid, each square is 1 unit. Let's take two points: (0, 2) and (10, 7)? Wait, no, from (0,2) to (10,7) is 5 up and 10 right, so slope 5/10 = 1/2. Alternatively, ( -10, -3)? Wait, maybe ( -10, -5) is wrong. Wait, let's take ( -10, -5) and (10, 7): difference in y is 12, difference in x is 20, 12/20 = 3/5? No, that's not right. Wait, maybe the correct points are (0, 2) and (10, 7)? Wait, no, looking at the graph, the blue line \( L_1 \) passes through (0, 2) and (10, 7)? Wait, no, when x=10, y=7? Wait, the top right arrow is at (10,7)? Wait, the grid: x from -10 to 10, y from -10 to 10. Let's take (0, 2) and (10, 7): rise is 5, run is 10, so slope 5/10 = 1/2. Alternatively, ( -10, -3) and (10, 7): rise 10, run 20, slope 10/20 = 1/2. Yes, that's correct. So the slope is 1/2.

Wait, maybe a better way: pick two points on \( L_1 \). Let's say (0, 2) and (10, 7). Then:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify points

Let \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (10, 7)\).

Step3: Calculate slope

Substitute into the formula: \( m = \frac{7 - 2}{10 - 0} = \frac{5}{10} = \frac{1}{2} \).

Answer:

\(\frac{1}{2}\)