Question

Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3,-1). Write your final equation in slope-intercept form.

Answer 1

you know the point slope formula?

Answer 2

isnt it like y=mx+b

Answer 3

no

Answer 4

that is the "slope intercept" form
\[\large y=\color{blue}mx+\color{red}b\] the slope is \(\color{blue}m\) and the y interecept is \(\color{red}b\)

Answer 5

what you want is the formula that uses a point \((\color{green}{x_1}, \color{magenta}{y_1})\) and a slope \(\color{blue}m\)

Answer 6

that formula is \[\large y-\color{magenta}{y_1}=\color{blue}m(x-\color{green}{x_1})\]

Answer 7

oh geez, I'm confused...can you walk me through?

Answer 8

point slope formula, what you use if you are given a point and a slope
it is \[\large y-\color{magenta}{y_1}=\color{blue}m(x-\color{green}{x_1})\] your point is \( (\color{green}{-3},\color{magenta}{-1})\) and youir slope is \(\color{blue}{\frac{2}{3}}\)

Answer 9

put the numbers in the slots, then some algebra

Answer 10

So I would have to find the other coordinate right?

Answer 11

no not at all

Answer 12

there is no "other coordinate"
but the three numbers in the place where they go
i color coded them for you

Answer 13

*put

Answer 14

y - -1=2/3(x - -3)

Answer 15

yes that is a start

Answer 16

then change both \(--\) to a \(+\)

Answer 17

y+-1=2/3(x+-3)
???

Answer 18

no
get rid of BOTH minus signs, make them one plus sign

Answer 19

so there will no longer be negatives

Answer 20

the same way that \[5-(-4)=5+4\]

Answer 21

zactly

Answer 22

sooo y+1=2/3(x+3)

Answer 23

yes

Answer 24

not done yet, but you did accomplish the first part
"Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3,-1)."

Answer 25

next you have to
"Write your final equation in slope-intercept form."

Answer 26

so now we do slope-intercept?

Answer 27

ok

Answer 28

two steps, always the same, to turn \[y-y_1=m(x-x_1)\] in to \[y=mx+b\]

Answer 29

first, the distributive property on the right \[y+1=\frac{2}{3}(x+3)\] distribute the \(\frac{2}{3}\)
i.e. get rid of the parentheses on the right

Answer 30

y+1=2/3x+3

Answer 31

yes good

Answer 32

second step, subtract 1 from both sides to get y by itself on the left

Answer 33

oops nope sorry, not quite right

Answer 34

\[\frac{2}{3}\times 3=2\]

Answer 35

im confused lol

Answer 36

so \[y+1=\frac{2}{3}(x+3)\\
y+1=\frac{2}{3}x+2\]

Answer 37

-1 to only one side??

Answer 38

subtract 1 from both sides now

Answer 39

y+1-1=2/3x+2-1
y=2/3x+1

Answer 40

yup

Answer 41

is that it?

Answer 42

yes, now you are done
it looks like \[y=mx+b\]

Answer 43

yay! thank you so much, you really helped me understand the concept.

Answer 44

yw
good luck!