Question

ation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -6)\) (the y - intercept) and \((2, -1)\) (we can also use other points like \((4, 4)\) or \((6, 9)\)). Let's use \((0, -6)\) and \((2, -1)\).

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 \((x_2,y_2)=(2, -1)\). Then \(m=\frac{-1-(-6)}{2 - 0}=\frac{-1 + 6}{2}=\frac{5}{2}\).

Step3: Determine the y - intercept \(b\)

The slope - intercept form of a line is \(y=mx + b\). We know that when \(x = 0\), \(y=-6\) (from the point \((0,-6)\)). Substituting \(x = 0\), \(y=-6\) and \(m=\frac{5}{2}\) into \(y=mx + b\), we get \(-6=\frac{5}{2}(0)+b\), so \(b=-6\).

Step4: Write the equation in slope - intercept form

Substitute \(m = \frac{5}{2}\) and \(b=-6\) into \(y=mx + b\). We get \(y=\frac{5}{2}x-6\).

Answer:

\(y=\frac{5}{2}x - 6\)