Find equations of the lines passing through (−2, 3) and having the following characteristics.

a.y=13/16x+37/8

b.y=3/2x+6

c.y=3/4x+9/2

d.x=-2

Step-by-step explanation:

All lines must pass through (-2,3)

a. The slope must be 13/16;

y=13/16x+b, SInce it must pass through (-2,3), plug in -2 as the x-value and 3 as the y-value

3=13/16(-2)+b, solve for b.

24/8=-13/8+b

37/8=b

y=13/16x+37/8

b, It must be parallel to the line 3x-2y=2; first, find the slope by converting to y=mx+b

3x-2y=2

-2y=-3x+2

y=3/2x-1, Parallel lines have the same slope so a line parallel to 3x-2y=2 and passing through (-2,3) will have a slope of 3/2.

Plug in (-2,3) to find the b-value again.

(3)=3/2(-2)+b

3=-3+b

6=b

y=3/2x+6

c. It must have a line perpendicular to 4x+3y=6.  Again like in b, find the slope.

y=-4/3+2, the slope is -4/3.

Now, perpendicular lines have the opposite inverse slopes which means that you add a negative sign and flip the numerator and denominator

-(-3/4), this is just 3/4

Ok, the slope of the line is 3/4, plug in (-2,3) to find the b-value again.

(3)=3/4(-2)+b

6/2=-3/2+b

9/2=b

y=3/4x+9/2

d. The line is paralell to the y-axis.

This just means that the line is vertical. The line has no slope.

The vertical line that passes through the x-value -2 is x=-2

x=-2

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:

step-by-step explanation:

; fx