Question

Is this correct: y=6x-33
Write an equation in slope intercept form the line passing through each pair of points.
(6,3)(-6,9)

Answer 1

Give me a second to see :)

Answer 2

k

Answer 3

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 3}})\quad &({\color{red}{ -6}}\quad ,&{\color{blue}{ 9}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 4

She is wanting slope-intercept form lol

Answer 5

It is incorrect. Try again using the slope formula @jdoe0001 gave you ;)

Answer 6

\[m=\frac{ 9-3 }{ -6-6} =\frac{ 6 }{ 0 }=6\]

Answer 7

-6-6 is not 0.

Answer 8

And even if it was, that would not work....anything over 0 does not work, but 0 over anything does.

Answer 9

-6-6= -12

Answer 10

correct!

Answer 11

so 6/-12 simplifies to what?

Answer 12

1/2

Answer 13

simplified

Answer 14

close....-1/2

Answer 15

ohh now \[y=-\frac{ 1 }{ 2 }x+b\]

Answer 16

yes. now plug in one ordered pair, and what do you get for b?

Answer 17

(6,3)

Answer 18

\[3=-\frac{ 1 }{ 2 }(6)+b\]

Answer 19

correct. now what is -1/2*6?

Answer 20

\[3=\frac{ 6 }{ 12 }\]

Answer 21

6/12? How'd you get that?

Answer 22

I always get confused on this part. I multiplied

Answer 23

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 3}})\quad &({\color{red}{ -6}}\quad ,&{\color{blue}{ 9}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ 9}}-{\color{blue}{ 6}}}{{\color{red}{ -6}}-{\color{red}{ 6}}}\implies \cfrac{\cancel{ 6}}{\cancel{ -12}}\implies -\cfrac{1}{2}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 3}}={\color{green}{ -\cfrac{1}{2}}}(x-{\color{red}{ 6}})\implies y-3= -\cfrac{1}{2}x+\left(-\cfrac{1}{2}\cdot -6\right)
\\ \quad \\
y-3= -\cfrac{1}{2}x+\left(-\cfrac{-6}{2}\cdot \right)\implies y-3= -\cfrac{1}{2}x+\left(\cfrac{\cancel{ -6}}{\cancel{ -2}} \right)\)

Answer 24

lol -(6/2)

what is that?

Answer 25

-(6/2) is just another way of saying -1/2(6)

Answer 26

@jdoe0001, would you mind finishing using the slope-intercept form so it's easier for her?

Answer 27

anyhow -6/-2 = +3
thus
\(\bf slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ 9}}-{\color{blue}{ 6}}}{{\color{red}{ -6}}-{\color{red}{ 6}}}\implies \cfrac{\cancel{ 6}}{\cancel{ -12}}\implies -\cfrac{1}{2}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 3}}={\color{green}{ -\cfrac{1}{2}}}(x-{\color{red}{ 6}})\implies y-3= -\cfrac{1}{2}x+\left(-\cfrac{1}{2}\cdot -6\right)
\\ \quad \\
y-3= -\cfrac{1}{2}x+\left(-\cfrac{-6}{2}\cdot \right)\implies y-3= -\cfrac{1}{2}x+\left(\cfrac{\cancel{ -6}}{\cancel{ -2}} \right)
\\ \quad \\
y-3= -\cfrac{1}{2}x+3\implies y\cancel{ -3+3}=-\cfrac{1}{2}x+3+3
\\ \quad \\
y=-\cfrac{1}{2}x+6\)

Answer 28

Thanks
@haleyelizabeth2017 and @jdoe0001
I now understand!!

Answer 29

yw

Answer 30

You are welcome.... :) but @jdoe0001 did most of the work :)

Answer 31

:D