Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-1, 0)\) and \((7, -4)\).

Step2: Calculate the slope (\(m\))

The formula for slope is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1) = (-1, 0)\) and \((x_2, y_2) = (7, -4)\). Then:
\(m = \frac{-4 - 0}{7 - (-1)} = \frac{-4}{8} = -\frac{1}{2}\)

Step3: Use the point - slope form to find the equation

The point - slope form of a line is \(y - y_1 = m(x - x_1)\). We can use the point \((-1, 0)\) and \(m = -\frac{1}{2}\).
Substitute into the formula: \(y - 0 = -\frac{1}{2}(x - (-1))\)
Simplify: \(y = -\frac{1}{2}(x + 1)\)
Expand: \(y = -\frac{1}{2}x-\frac{1}{2}\)

Answer:

\(y = -\frac{1}{2}x-\frac{1}{2}\)