Question

fill in the blank 3 points in fraction form (example, 2/3), find the slope of the line. write the slope of a line parallel and the slope of a line perpendicular to the given line. the slope of the line is type your answer... the slope of the parallel line is type your answer... the slope of the perpendicular line is type your answer...

Explanation:

Step1: Select two points on the line

Let's take two points \((x_1,y_1)\) and \((x_2,y_2)\) on the given line. From the graph, we can take \((0, 3)\) and \((4, - 1)\).

Step2: Calculate the slope of the given line

The slope - formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1 = 3,x_2=4,y_2=-1\) into the formula, we get \(m=\frac{-1 - 3}{4-0}=\frac{-4}{4}=-1\).

Step3: Find the slope of the parallel line

Parallel lines have the same slope. So the slope of the parallel line is \(m_{parallel}=-1\).

Step4: Find the slope of the perpendicular line

The product of the slopes of two perpendicular lines is \(- 1\). Let the slope of the perpendicular line be \(m_{perpendicular}\). Since \(m\times m_{perpendicular}=-1\) and \(m = - 1\), then \((-1)\times m_{perpendicular}=-1\), so \(m_{perpendicular}=1\).

Answer:

The slope of the line: -1
The slope of the parallel line: -1
The slope of the perpendicular line: 1