Question

what is the y - value of this function when x = 2?

Explanation:

Step1: Find the equation of the line

First, we identify two points on the line. From the graph, we can see that the line passes through \((-2, 0)\) and \((0, -3)\) (wait, actually, looking at the y-intercept, when \(x = 0\), \(y=-3\)? Wait, no, let's check again. Wait, the line crosses the y-axis at \((0, -3)\)? Wait, no, looking at the grid, when \(x = 0\), the y-coordinate is -3? Wait, no, maybe I made a mistake. Wait, let's take two clear points. Let's see, when \(x=-2\), \(y = 0\), and when \(x = 0\), \(y=-3\)? Wait, no, let's calculate the slope. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((-2, 0)\) and \((0, -3)\). Then \(m=\frac{-3 - 0}{0 - (-2)}=\frac{-3}{2}=-1.5\). So the equation of the line is \(y=mx + b\), where \(b\) is the y-intercept. When \(x = 0\), \(y=-3\), so \(b=-3\). So the equation is \(y=-1.5x - 3\).

Step2: Substitute \(x = 2\) into the equation

Now, substitute \(x = 2\) into \(y=-1.5x - 3\). So \(y=-1.5(2)-3=-3 - 3=-6\). Wait, but let's check the graph again. Wait, maybe my initial points are wrong. Wait, let's look at the line again. When \(x = -2\), \(y = 0\); when \(x = 0\), \(y=-3\)? Wait, no, maybe the y-intercept is at \((0, -3)\)? Wait, but when \(x = 2\), let's count the grid. Each grid square is 1 unit. So from \(x = 0\), moving 2 units to the right (x=2), and since the slope is -1 (wait, maybe I miscalculated the slope). Wait, let's take two points: \((-2, 0)\) and \((0, -2)\)? Wait, no, the line crosses the y-axis at (0, -3)? Wait, no, looking at the graph, when x=0, the y-coordinate is -3? Wait, no, maybe the line is \(y=-x - 3\)? Wait, no, let's check the slope again. Let's take (x1, y1)=(-2, 0) and (x2, y2)=(0, -3). Then slope m=( -3 - 0)/(0 - (-2))= -3/2= -1.5. So equation is y= -1.5x - 3. Then when x=2, y= -1.5*2 -3= -3 -3= -6. But let's check the graph. From x=0 (y=-3), moving 2 units right (x=2), and since the slope is -1.5, which is -3/2, so for each 2 units right, y decreases by 3. So from x=0 (y=-3), x=2, y=-3 -3= -6. So that's correct.

Answer:

-6