Question

find an equation for the line below.

Explanation:

Step1: Identify two points

From the graph, we can see two points: let's take \((-5, 1)\) and \((-1, 3)\) (we can verify these by looking at the grid intersections).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(-5,1)\) and \((x_2,y_2)=(-1,3)\), we get:

$$ m=\frac{3 - 1}{-1 - (-5)}=\frac{2}{4}=\frac{1}{2} $$

Step3: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((-1,3)\) and \(m = \frac{1}{2}\).

$$ y - 3=\frac{1}{2}(x - (-1)) $$

Simplify the equation:

$$ y - 3=\frac{1}{2}(x + 1) $$

$$ y - 3=\frac{1}{2}x+\frac{1}{2} $$

Add 3 to both sides:

$$ y=\frac{1}{2}x+\frac{1}{2}+3 $$

$$ y=\frac{1}{2}x+\frac{1 + 6}{2} $$

$$ y=\frac{1}{2}x+\frac{7}{2} $$

(We can also verify with another point. Let's check the \(y\)-intercept. When \(x = 0\), \(y=\frac{7}{2}=3.5\), which matches the graph as the line crosses the \(y\)-axis around \(y = 3.5\))

Answer:

The equation of the line is \(y=\frac{1}{2}x+\frac{7}{2}\) (or \(y = 0.5x+3.5\))