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thomas49th
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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
Last edited:
HallsofIvy said:and parallel if and only if (m_{1})(m_{2})= -1.
cant it beperpendicular if and only if (m1)(m2)= -1.
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.
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.
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.
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.
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.