Finding the equation of a line perpendicular to a given line passing through a given point
Find the equation of the line perpendicular to
The first step is to write the equation in slope-intercept form.
We see that the slope is
This means that the slope of the line perpendicular to the given line is the negative reciprocal, or
Next, we use the point-slope formula with this new slope and the given point.
We can solve linear equations in one variable in the form
using standard algebraic properties. See
[link] and
[link].
A rational expression is a quotient of two polynomials. We use the LCD to clear the fractions from an equation. See
[link] and
[link].
All solutions to a rational equation should be verified within the original equation to avoid an undefined term, or zero in the denominator. See
[link] and
[link].
Given two points, we can find the slope of a line using the slope formula. See
[link] .
We can identify the slope and
y -intercept of an equation in slope-intercept form. See
[link].
We can find the equation of a line given the slope and a point. See
[link].
We can also find the equation of a line given two points. Find the slope and use the point-slope formula. See
[link].
The standard form of a line has no fractions. See
[link] .
Horizontal lines have a slope of zero and are defined as
where
c is a constant.
Vertical lines have an undefined slope (zero in the denominator), and are defined as
where
c is a constant. See
[link].
Parallel lines have the same slope and different
y- intercepts. See
[link] .
Perpendicular lines have slopes that are negative reciprocals of each other unless one is horizontal and the other is vertical. See
[link] .
Section exercises
Verbal
What does it mean when we say that two lines are parallel?
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
