Question

what is the equation of the line parallel to the line y = 2x + 3 that passes through the point 1,4 in slope intercept form?

Answer 1

@jim_thompson5910

Answer 2

what is the slope of the given line

Answer 3

?

Answer 4

what is the equation of the given line

Answer 5

y = 2x+3?

Answer 6

what is the slope of that line

Answer 7

hint: y = mx+b has a slope of m

Answer 8

I have no idea.. do I input something?

Answer 9

in y = 2x+3, what is the number in front of the x variable?

Answer 10

2

Answer 11

so that is the slope

Answer 12

any line parallel to y = 2x+3 will also have a slope of 2

Answer 13

since parallel lines have equal slopes

Answer 14

Right.. but how do I figure out the equation?

Answer 15

how would you find the equation of the line if you knew the slope and a point that goes through it?

Answer 16

I don't remember this at all

Answer 17

we know that m = 2

we also know that x = 1 and y = 4 since we have the point (1,4) on this parallel line

Answer 18

so...

y = mx+b

y = 2x + b ... plug in m = 2

4 = 2*1 + b ... plug in x = 1 and y = 4

solve for b

Answer 19

Oh so you plug it in.. okay. 4 = b + 2

Answer 20

which means b = ???

Answer 21

2?

Answer 22

good, the equation of the parallel line is y = 2x + 2

Answer 23

Can we do one other for practice?

Answer 24

sure

Answer 25

One sec.. so... What is the equation of the line perpendicular to the line y = 2x + 3 that passes through the point (1,4) in point-slope form?
Would we use the same formula?

Answer 26

it's a bit different with perpendicular lines

Answer 27

the given slope is 2, which is really 2/1

flip the fraction: 2/1 -----> 1/2

flip the sign: 1/2 ----> -1/2

Answer 28

so the perpendicular slope is -1/2

Answer 29

so we know that

m = -1/2
x = 1
y = 4


plug them all into y = mx + b

then solve for b

Answer 30

4 = -1/2(1) + b
b = 9/2
would it be...
y - 4 = -1/2(x-1)?

Answer 31

you could use point slope form

now get it into slope intercept form

Answer 32

oh i see what you mean

Answer 33

you got b = 9/2, so the equation in slope intercept form is

\[\large y = -\frac{1}{2}x + \frac{9}{2}\]

Answer 34

you could write it in point slope form to get

y - 4 = -1/2(x-1)

Answer 35

so I could use that solution?

Answer 36

either one works, it will depend on what your book or teacher wants

Answer 37

Yeah, I think the second one is what she wants. Thanks again. :)

Answer 38

you're welcome