Question

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? Line $1 :$ Passes through $(2,3)$ and $(4,-1)$ Line $2 :$ Passes through $(6,3)$ and $(8,5)$

Name: Problem 96, Chapter 2: Precalculus
Uploaded: 2019-08-01T18:22:32-08:00
Duration: 1 min 14 s
Channel: Mariam Saleh-Esa
Description: For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? Line 1 : Passes through (2,3) and (4,-1) Line 2 : Passes through (6,3) and (8,5)

   For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
Line $1 :$ Passes through $(2,3)$ and $(4,-1)$
Line $2 :$ Passes through $(6,3)$ and $(8,5)$

Precalculus

Jay Abramson 1st Edition

Chapter 2, Problem 96

Instant Answer

Solved by Expert Mariam Saleh-Esa

08/01/2019

Step 1

The formula for the slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Show more…

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For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? Line $1 :$ Passes through $(2,3)$ and $(4,-1)$ Line $2 :$ Passes through $(6,3)$ and $(8,5)$

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Key Concepts

Slope Calculation

The slope of a line is determined by the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). This is typically calculated using the formula (y2 - y1)/(x2 - x1) by taking any two points on the line. It is a fundamental concept in coordinate geometry for understanding line steepness and direction.

Parallel Lines

Parallel lines have the same slope, which means that they do not intersect because they rise and run at the same rate. Determining whether two lines are parallel involves comparing their slopes, and if the slopes are equal, the lines are parallel.

Perpendicular Lines

Perpendicular lines intersect at right angles (90 degrees), and their slopes are negative reciprocals of each other. This means if one line has a slope m, the slope of a line perpendicular to it must be -1/m. This relationship is key in verifying perpendicularity in coordinate geometry.

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