Question

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Explanation:

To determine the equation of the line, we can use the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step 1: Find the y - intercept (\(b\))

The y - intercept is the point where the line crosses the y - axis. From the graph, we can see that the line crosses the y - axis at \((0,-2)\). So, \(b=-2\).

Step 2: Calculate the slope (\(m\))

We can use two points on the line to calculate the slope. Let's use the points \((0, - 2)\) and \((1, - 1)\) (we can also use other pairs of points). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1 = 0,y_1=-2,x_2 = 1,y_2=-1\) into the formula:
\(m=\frac{-1-(-2)}{1 - 0}=\frac{-1 + 2}{1}=\frac{1}{1}=1\)

Step 3: Write the equation of the line

Now that we know \(m = 1\) and \(b=-2\), we substitute these values into the slope - intercept form \(y=mx + b\).
We get \(y=1\times x-2\), or \(y=x - 2\)

Answer:

The equation of the line is \(y=x - 2\)