Question

write the equation of this line in slope - intercept form.

Explanation:

1. First, identify two points on the line:

• Let's assume two points on the line are \((0, - 6)\) (the y - intercept, where \(x = 0\)) and \((6,-5)\).

1. Then, calculate the slope \(m\) using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\):

• Here, \(x_1 = 0,y_1=-6,x_2 = 6,y_2=-5\).
• \(m=\frac{-5-(-6)}{6 - 0}=\frac{-5 + 6}{6}=\frac{1}{6}\).

1. Recall the slope - intercept form of a line:

• The slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
• We found \(m=\frac{1}{6}\) and \(b=-6\).
• So the equation of the line is \(y=\frac{1}{6}x-6\).

Step1: Select two points

Selected \((0, - 6)\) and \((6,-5)\) on the line.

Step2: Calculate the slope

Used \(m=\frac{y_2 - y_1}{x_2 - x_1}\), so \(m=\frac{-5-(-6)}{6 - 0}=\frac{1}{6}\).

Step3: Write the equation

Substituted \(m=\frac{1}{6}\) and \(b = - 6\) into \(y=mx + b\) to get \(y=\frac{1}{6}x-6\).

Answer:

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