Problem 87
Question
If two lines are parallel, describe the relationship between their slopes.
Step-by-Step Solution
Verified Answer
The slopes of two parallel lines are always equal.
1Step 1: Understanding Parallel lines
Parallel lines are two lines in a plane that do not intersect or touch each other at any point. They are always the same distance apart.
2Step 2: Concept of Slope
The slope of a line, often represented by the letter 'm', can be defined as the rate at which y changes as x changes in a given line. It is usually calculated as 'rise over run' which means the ratio of the vertical change to the horizontal change.
3Step 3: Relationship between slopes of Parallel lines
The slopes of two parallel lines are always equal. If two lines are parallel, and their slopes are m1 and m2, then \( m1 = m2 \). This is due to the fact that parallel lines have the same steepness and they run in the same direction.
Other exercises in this chapter
Problem 86
Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.
View solution Problem 86
The number of lawyers in the United States can be modeled by the function $$ f(x)=\left\\{\begin{array}{ll} 6.5 x+200 & \text { if } 0 \leq x
View solution Problem 87
The number of lawyers in the United States can be modeled by the function $$ f(x)=\left\\{\begin{array}{ll} 6.5 x+200 & \text { if } 0 \leq x
View solution Problem 88
If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation.
View solution