Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Graphing Horizontal and Vertical Lines

Graphing Horizontal and Vertical Lines 1.3 - Solution

arrow_back Return to Graphing Horizontal and Vertical Lines
a
We want to use the slope formula to find the slope of the line that passes through the given points.

m=y2y1x2x1\begin{gathered} m = \dfrac{y_2-y_1}{x_2-x_1} \end{gathered} In the above formula, mm represents the slope, and (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) two points on the line.

Calculating Slope

In this exercise, we are given the points (-3,-1)(\text{-}3,\text{-}1) and (5,-1).(5,\text{-}1). Note that, when substituting these values into the slope formula, it doesn't matter which point we choose to use as (x1,y1)({\color{#0000FF}{x_1}},{\color{#0000FF}{y_1}}) or (x2,y2).({\color{#009600}{x_2}},{\color{#009600}{y_2}}). m=115(-3)orm=-11-35\begin{gathered} m=\dfrac{{\color{#009600}{1}}-{\color{#0000FF}{1}}}{{\color{#009600}{5}}-({\color{#0000FF}{\text{-}3}})} \quad \text{or} \quad m=\dfrac{\phantom{\text{-}}{\color{#009600}{1}}-{\color{#0000FF}{1}}}{{\color{#009600}{\text{-}3}}-{\color{#0000FF}{5}}} \end{gathered} Both will give the same result. Here we will use the points in the given order and solve for the slope m.m.
m=y2y1x2x1m = \dfrac{y_2-y_1}{x_2-x_1}
m=115(-3)m=\dfrac{{\color{#009600}{1}}-{\color{#0000FF}{1}}}{{\color{#009600}{5}}-({\color{#0000FF}{\text{-}3}})}
Evaluate right-hand side
m=115+3m=\dfrac{1-1}{5+3}
m=08m=\dfrac{0}{8}
m=0m=0
The slope of the line that passes through the given points is 0.0. This means that as xx increases, yy neither increases nor decreases. Therefore, we have a horizontal line.

Check by Graphing

Finally, let's plot the given points and connect them with a line to check if the direction of the slope matches what we calculated above.

Observing the graph, we can confirm that as xx moves in the positive direction, yy does not move in the positive or negative direction.

b
We'll use the slope formula to calculate the slope of the line, using the two given points.
m=y2y1x2x1m=\dfrac{y_2-y_1}{x_2-x_1}
m=0.50.502m=\dfrac{{\color{#009600}{0.5}}-{\color{#0000FF}{0.5}}}{{\color{#009600}{0}}-{\color{#0000FF}{2}}}
Evaluate right-hand side
m=0.50.502m=\dfrac{0.5-0.5}{0-2}
m=0-2m=\dfrac{0}{\text{-}2}
m=0m=0
A slope of 00 means that for every 11 horizontal step, we take 00 vertical steps. Therefore, we have a horizontal line. The line can be graphed by drawing a line through the two points.