Explaining Perpendicular Line to y=3x+4

In summary, the conversation discusses the relationship between two perpendicular lines and their gradients. The condition for two lines to be perpendicular is that their gradients must satisfy the equation (m1)(m2) = -1. This can be derived from properties of the tangent function and can also be seen by graphing perpendicular lines.
  • #1
thomas49th
655
0

Homework Statement


The line l has equation y = 3x + 4
Cans someone xplain how [tex]y = -\frac{1}{3}x-4[/tex] is perpendicular to line l(bisects l at 90°)

Homework Equations



y = mx + c
 
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  • #2
What condition must the gradients of two perpendicular lines satisfy?
 
  • #3
negtive gradient.

y = mx + c where m is a negitive number?
 
  • #4
No, remember that the slope of a line is the tangent of the angle the line makes with the x-axis. If two lines are y= m1x+ b and y= m2x+ c, then the two lines are parallel if and only if m1= m2 and parallel if and only if (m1)(m2)= -1.

Those can both be derived from properties of the tangent function.
 
  • #5
HallsofIvy said:
and parallel if and only if (m1)(m2)= -1.

Just correcting a typo: you mean perpendicular if and only if (m1)(m2)= -1.
 
  • #6
perpendicular if and only if (m1)(m2)= -1.
cant it be

perpendicular if and only if (m1)(m2)= -0.5? Or any other number there? Was that just an example? If not what is so special about -1?

(m1)(m2)= -1
so 3 * -1/3 = -1

cheerz, Big help
 
  • #7
Graph a set of perpendicular intersecting lines.

Now using the graphs, compute the slopes, can you now see why the relationship is [itex] m_1 m_2 = -1 [/itex]

You may need to look at several sets of lines to see the relationships.
 
  • #8
Thomas49th, are you saying you cannot read our responses?
 
  • #9
aha, ingenius. It works. Thanks a load :cool:
 

1. What is the equation for a perpendicular line to y=3x+4?

The equation for a perpendicular line to y=3x+4 will have a slope that is the negative reciprocal of 3, which is -1/3. It will also have a different y-intercept than 4, depending on the specific point that the perpendicular line passes through.

2. How do you determine if two lines are perpendicular?

To determine if two lines are perpendicular, you can use the slope formula to calculate the slopes of each line. If the slopes are negative reciprocals of each other, then the lines are perpendicular. Another way to determine perpendicularity is by looking at the equations of the lines. If one line has a slope of m and the other has a slope of -1/m, then they are perpendicular.

3. Can you explain the concept of perpendicular lines visually?

Perpendicular lines are two lines that intersect at a 90 degree angle. If you were to draw two intersecting lines and measure the angles formed at the point of intersection, you would find that they are both 90 degrees. This is a visual representation of perpendicular lines.

4. How do you graph a line that is perpendicular to y=3x+4?

To graph a line that is perpendicular to y=3x+4, you can start by plotting the y-intercept of (0,4). Then, using the negative reciprocal slope of -1/3, you can find another point on the line. For example, if you move one unit to the right and three units down from the y-intercept, you will have the point (1,1). Plot this point and draw a line through both points to create a perpendicular line to y=3x+4.

5. What is the purpose of understanding perpendicular lines in math?

Understanding perpendicular lines is important in math because it allows us to solve problems involving angles and intersecting lines. It is also a fundamental concept in geometry and is used in various real-world applications, such as engineering, architecture, and navigation.

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