Question

Write the equation of the line through (22, 4) that is parallel to the y=3 . Show your work.

Answer 1

If you have two lines
y = mx + c
y = nx + d

...what must be true if the lines are parallel? I.e., what can you say about m, n, c or d?

Answer 2

same slope

Answer 3

hint: two parallel lines have the same slope

Answer 4

Right, hence m and n is the same.

With the line, y = 4, what is the slope of that line?

Answer 5

the slope is 0 right

Answer 6

So if we write y = 4 in the form
y = mx + c,
what is m, the slope?

Answer 7

and its y=3

Answer 8

Yes, sorry, y = 3

y = 3 is the same as writing
y = 0x + 3
i.e., m = 0, c = 3. The slope is m = 0

So if we have a new line passing through (22,4), it must also have slope of zero.

What line with slope zero passes through (22,4)?

Answer 9

y = (something)x + (something)

Answer 10

but if a slope is 0 there is no rise over run

Answer 11

Yes, so it must be

y = 0x + (something)

i.e., y = something

What must that something be so the line passes through (22,4)?

Answer 12

it has to have the same slope?

Answer 13

Yes, that is why the coefficient of x, the number before the x, is zero.

Answer 14

but i dont get what the equation would be

Answer 15

just y=0x+3?

Answer 16

We know the slope must be zero. That is, for a straight line
y = mx + c
it must be that m = 0

That is, the line is of the form
y = 0x + c
i.e., y = 3

Yes, y = 0x + 3, is the first line.

Now what then must be the equation of the line parallel to this that passes through (22,4)?

It must have slope zero, hence we know the equation is of the form

y = 0x + c
for some value of c. What must that value of c be?

Answer 17

ohhhhh its 4=0x+22

Answer 18

or no?

Answer 19

Nooo ... the equation you just wrote down implies that 4 = 22, which is clearly false.

y = 0x + c
and passes through (22,4), which means that (x,y) = (22,4) satisfies that equation.

Answer 20

Substitute x = 22, y = 4 into the equation
y = 0x + c
and solve for c

Answer 21

im so CONFUSED NOW :(

Answer 22

OHHHHH OKAY!

Answer 23

C=4

Answer 24

That dot is the point (22,4). What straight line passes through that point parallel to y = 4?

Yes,
y= 0x + 4
i.e., y = 4

Answer 25

SO THAT WOULD BE MY EQQUATION RIGHT

Answer 26

Yes,
y = 4

Answer 27

BUT IF ITS AN EQAUTION WHY CANT I RIGHT IT LIKE Y=0X+4

Answer 28

You can write it as y = 0x + 4 if you like.

Answer 29

But as 0x = 0 for all values of x, it is simpler to write y = 4

Answer 30

oh i see! THANK YOOU SO MUCH! youre literally a better teacher than my own teacher

Answer 31

thanks