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Chapter 2: Problem 31

If two lines are parallel, describe the relationship between their slopes.

Short Answer

Expert verified
If two lines are parallel, their slopes are equal.

Step by step solution

01

Concept of Parallel Lines

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that are both infinite and never intersect. In the context of a Cartesian plane, this means that the lines never cross each other no matter how extended.
02

Slope of a Line

The slope of a line, in mathematics, is a measure of the direction and steepness of a line. It can be computed using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line and \(m\) is the slope.
03

Relationship Between Slopes of Parallel Lines

For two lines to be parallel, their slopes must be equal. This is because slope is a measure of direction and steepness of a line, so two lines with the same slope will have the same direction and will therefore not intersect or cross each other. Hence, if two lines are parallel, their slopes will be equal.

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Most popular questions from this chapter

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} (x-2)^{2}+(y+3)^{2} &=4 \\ y &=x-3 \end{aligned} $$

use a graphing utility to graph each circle whose equation is given. $$ x^{2}+y^{2}=25 $$

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+y^{2}=49 $$

Exercises \(129-131\) will help you prepare for the material covered in the next section. The function \(C(t)=20+0.40(t-60)\) describes the monthly cost, \(C(t),\) in dollars, for a cellphone plan for \(t\) calling minutes, where \(t>60 .\) Find and interpret \(C(100)\)

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=16 \\ x-y &=4 \end{aligned} $$
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