Question

write the equation of the line in fully simplified slope - intercept form. answer attempt 1 out of 2 answer:

Explanation:

Step1: Identify two points on the line

Let's take two points \((x_1,y_1)\) and \((x_2,y_2)\) from the graph. For example, \((0, - 4)\) and \((6,-3)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((0,-4)\) and \((6,-3)\) gives \(m=\frac{-3-(-4)}{6 - 0}=\frac{-3 + 4}{6}=\frac{1}{6}\).

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

The y - intercept is the y - value when \(x = 0\). From the point \((0,-4)\), \(b=-4\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=\frac{1}{6}\) and \(b = - 4\) gives \(y=\frac{1}{6}x-4\).

Answer:

\(y=\frac{1}{6}x - 4\)