Question

(b)
y =
blue box × red cross

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the y - intercept (0, - 6) and the point (2, - 4).

Step2: Calculate the slope (m)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 6)\) and \((x_2,y_2)=(2, - 4)\). Then \(m=\frac{-4-(-6)}{2 - 0}=\frac{-4 + 6}{2}=\frac{2}{2}=1\)? Wait, no, wait. Wait, the end - point is at (2, - 4)? Wait, no, looking at the graph again, the black dot is at (2, - 4)? Wait, no, the x - coordinate of the black dot: from the grid, the x - value is 2, y - value is - 4? Wait, no, maybe I misread. Wait, the y - axis: the grid lines, each grid is 1 unit. Wait, the line goes from the left (let's take a point on the left, say when x=-6, what's y? Wait, no, the line has a black dot at (2, - 4)? Wait, no, let's check the y - intercept. The line crosses the y - axis at (0, - 6). Then the other point: the black dot is at (2, - 4)? Wait, no, slope calculation: if we take two points, (0, - 6) and (2, - 4). Then \(m=\frac{-4-(-6)}{2-0}=\frac{2}{2}=1\)? But the line looks like a curve? Wait, no, maybe it's a logarithmic or exponential? Wait, no, maybe it's a linear function? Wait, no, the graph is a curve? Wait, the user might have a linear function? Wait, no, the graph is a curve, maybe a logarithmic function. Wait, let's re - examine.

Wait, maybe the function is of the form \(y = \frac{1}{2}x-6\)? Wait, no, let's check the point (2, - 4). If \(x = 2\), then \(y=\frac{1}{2}(2)-6=1 - 6=-5\), no. Wait, maybe the slope is \(\frac{1}{2}\). Wait, from (0, - 6) to (2, - 5)? No, the black dot is at (2, - 4). Wait, maybe the equation is \(y=\frac{1}{2}x - 6\)? No, that won't give (2, - 4). Wait, \(y=\frac{1}{2}x-5\)? When \(x = 0\), \(y=-5\), no. Wait, maybe the function is \(y=\log(x + 1)-6\)? No, that's complicated. Wait, maybe it's a linear function. Wait, let's take two points: (0, - 6) and (2, - 4). The slope is \(\frac{-4+6}{2 - 0}=1\). So the equation would be \(y=x - 6\). Let's check \(x = 2\), \(y=2 - 6=-4\), which matches the black dot. So the equation is \(y=x - 6\).

Answer:

\(y = x-6\)