Write an equation of the line perpendicular to the given line that contains p. p(4, -3); y=1/2x+3. write an equation for the line in point-slope form.

y = 2x - 5

Step-by-step explanation:

First, we must find the slope of the current equation.

This is the number in front of the x.

Seeing as this is 1/2x, the slope of this line is 1/2

When finding the slope of a line perpendicular, you need to find the

So, in this case it is:

This gives the result -2, so the gradient on the perpendicular line is -2

Now, to find the equation of a line, you need to use:

y - y1 = m(x - x1)

Where y1 and x1 are the values in the coordinates (4 , -3)

So y1  = -3, x1 = 4, and m is a half. Plug these values in:

y - 3 =2(x - 4)

Expand the brackets by multiplying the contents by two:

x * 2 = 2x

-4 * 2 = -8

2x - 8

y - 3 = 2x -8

And now simply move the -3 over to the other side, making it a positive:

y = 2x - 8 + 3

Simplify:

y = 2x - 5

So the equation of the line is y = 2x - 5

50x5=$250

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: