Question

question 22
22)m =

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: let's take \((-2, -4)\) and \((-1, 0)\) (or other clear points). Wait, actually, looking at the grid, let's find two distinct points. Let's take the lower point: when \(x = -3\) (wait, maybe better to take the intersection with x-axis and another point. Wait, the line passes through \((-2, 0)\)? No, wait, the arrow points: let's check the coordinates. Let's take the top point: let's say \((-1, 4)\) and the bottom point: \((-3, -4)\)? Wait, maybe better to use the two marked points. Wait, the line has a point at \((-1, 4)\) (top) and \((-3, -4)\)? No, maybe I misread. Wait, let's look at the grid. Each square is 1 unit. Let's take two points: let's say the line passes through \((-2, 0)\)? No, wait, the line goes through \((-1, 4)\) and \((-3, -4)\)? Wait, no, let's calculate the slope. The formula for slope \(m\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points: let's say the top point is \((-1, 4)\) and the bottom point is \((-3, -4)\)? Wait, no, maybe the two points are \((-1, 4)\) and \((-3, -4)\)? Wait, no, let's check the x and y axes. Wait, the x-axis is horizontal, y-axis vertical. Let's take two points: let's say when \(x = -1\), \(y = 4\) (top point) and when \(x = -3\), \(y = -4\) (bottom point). Then the change in y is \(4 - (-4)=8\), change in x is \(-1 - (-3)=2\), so slope would be \(8/2 = 4\)? Wait, no, maybe I got the points wrong. Wait, maybe the two points are \((-1, 4)\) and \((-2, 0)\)? No, let's look again. Wait, the line passes through \((-2, 0)\)? No, the line crosses the x-axis at \((-2, 0)\)? Wait, no, the line has a point at \((-1, 4)\) and \((-3, -4)\)? Wait, maybe the correct points are \((-1, 4)\) and \((-3, -4)\). Wait, no, let's count the rise over run. From the bottom point to the top point: how many units up and right? Let's say the bottom point is \((-3, -4)\) and the top point is \((-1, 4)\). Then the change in y is \(4 - (-4)=8\), change in x is \(-1 - (-3)=2\), so slope is \(8/2 = 4\)? Wait, that seems high. Wait, maybe the two points are \((-1, 4)\) and \((-2, 0)\). Then change in y is \(4 - 0 = 4\), change in x is \(-1 - (-2)=1\), so slope is \(4/1 = 4\). Wait, or maybe the points are \((-1, 4)\) and \((-3, -4)\), slope is \((4 - (-4))/(-1 - (-3))=8/2=4\). So the slope \(m = 4\). Wait, let's verify. If x increases by 1, y increases by 4. So from \((-3, -4)\) to \((-2, 0)\): y goes from -4 to 0 (increase by 4), x from -3 to -2 (increase by 1), so slope is 4/1=4. Yes, that makes sense. So the slope \(m\) is 4.

Step1: Identify two points on the line

Let's take two points on the line: \((-3, -4)\) (bottom) and \((-2, 0)\) (on x-axis).

Step2: Apply slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-3, -4)\) and \((x_2, y_2)=(-2, 0)\). Then:
\(m=\frac{0 - (-4)}{-2 - (-3)}=\frac{4}{1}=4\)

Answer:

\(4\)