Question

line ab passes through points a(-6, 6) and b(12, 3). if the equation of the line is written in slope-intercept form, $y = mx + b$, then $m = -\frac{1}{6}$. what is the value of $b$?
options: 6, -5, 5, -6

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-\frac{1}{6}\), and we can use a point on the line (either point \(A(-6,6)\) or point \(B(12,3)\)) to find the value of \(b\). Let's use point \(A(-6,6)\). Substitute \(x=-6\), \(y = 6\) and \(m=-\frac{1}{6}\) into the equation \(y=mx + b\).

Step2: Substitute values into the equation

Substituting into \(y=mx + b\), we get \(6=-\frac{1}{6}\times(-6)+b\).
First, calculate \(-\frac{1}{6}\times(-6)\). The product of two negative numbers is positive, and \(\frac{1}{6}\times6 = 1\). So the equation becomes \(6 = 1 + b\).

Step3: Solve for \(b\)

To solve for \(b\), subtract 1 from both sides of the equation \(6=1 + b\). We have \(b=6 - 1\).

Answer:

\(5\)