Question

find an equation for the line below.

Explanation:

Step1: Identify two points

From the graph, two points on the line are \((-5, 3)\) and \((1, 6)\).

Step2: Calculate the slope

The slope \(m\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points: \(m=\frac{6 - 3}{1 - (-5)}=\frac{3}{6}=\frac{1}{2}\).

Step3: Use point - slope form

Using the point \((1, 6)\) and slope \(m = \frac{1}{2}\), the point - slope form is \(y - y_1=m(x - x_1)\). So \(y - 6=\frac{1}{2}(x - 1)\).

Step4: Simplify to slope - intercept form

Expand the equation: \(y - 6=\frac{1}{2}x-\frac{1}{2}\). Then add 6 to both sides: \(y=\frac{1}{2}x-\frac{1}{2}+6=\frac{1}{2}x+\frac{11}{2}\) (or \(y = 0.5x+5.5\)).

Answer:

\(y=\frac{1}{2}x+\frac{11}{2}\) (or equivalent forms like \(y = 0.5x + 5.5\))