Question

Find the equation of the line.
A) y=-
3
-
2
x + 1
B) y=-
2
-
3
x - 1
C) y=
2
-
3
x + 1
D) y=
3
_
2
x - 1
http://www.usatestprep.com/modules/gallery/files/4/451/451.png
i took out b and c

Answer 1

hmmm when y = + 5 on that graphic, what is the value of x?

Answer 2

@jdoe0001 -1

Answer 3

check closely, notice the graph

Answer 4

@jdoe0001 so 0

Answer 5

notice where y is 5

Answer 6

oh ok i thought you mean on the x axis where it intercepts

Answer 7

so the x value is 5

Answer 8

hmmm is it? check closely where the line on the grid hits the x-axis

Answer 9

on the graph that i gave the link for it lines up perfectly with 5

Answer 10

hmmm it lines up with 5 on the y-axis, yes, but it hits the x-axis elsewhere

Answer 11

now im confused because the x axis has two side, negative and positive. on the negative side the lines goes through between -1 and 0

Answer 12

actually, it doesn't touch -1 on the x-axis, when the y-axis is 0
more like -1.5 or -1,5,0

but is not exact, reason why I asked on the y = +5 instead

since when y = +5 and -5, there's a defined x-axis value, check closely

Answer 13

6

Answer 14

yeap, is x = 6 when y = +5
what about when y = -5?

Answer 15

-9

Answer 16

yeap
so....now let us take a peek at those 2 points
6, 5 and
-9, -5

we'll need to get the slope first
one sec

Answer 17

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 6}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ -9}}\quad ,&{\color{blue}{ -5}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ -5}}-{\color{blue}{ 5}}}{{\color{red}{ -9}}-{\color{red}{ 6}}}\implies \cfrac{\cancel{-10}}{\cancel{-15}}\implies \cfrac{2}{3}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ 5}}={\color{green}{ \cfrac{2}{3}}}(x-{\color{red}{ 6}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 18

so if we change that to y=mx+b the answer would be C

Answer 19

well, dunno what C is, but let us see what it's by solving for "y" :)
\(\bf y-{\color{blue}{ 5}}={\color{green}{ \cfrac{2}{3}}}(x-{\color{red}{ 6}})\implies y=\cfrac{2}{3}x-\cfrac{2}{\cancel{3}}\cdot \cancel{6}+5
\\ \quad \\
y=\cfrac{2}{3}x-4+5\implies y=\cfrac{2}{3}x+1\)

Answer 20

thank you

Answer 21

yw