Question

The ordered pairs(2,-21) and (5,-45) are solutions to which of the following equations:

Y=-8x-5
Y=-8x+5
Y=8x-5
Y=8x+5

Answer 1

have you covered slopes yet?

Answer 2

I think so

Answer 3

plugin x and y values into the equations and see which one gives a true equality

Answer 4

Please guide me

Answer 5

so if those 2 points belong to whatever equation
that means that you'd want to find
the equation that passes through (2,-21) and (5,-45)

thus \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ -21}})\quad &({\color{red}{ 5}}\quad ,&{\color{blue}{ -45}})
\end{array}
\\\quad \\

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 \\

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} \)

will give you the equation

Answer 6

Ok let me check

Answer 7

P0stir0N@ I'm plugging in those digits into the equation, but It won't come out right

Answer 8

slope(m) = (y2 - y1) / (x2 - x1)
(2,-21)..x1 = 2 and y1 = -21)
(5,-45)..x2 = 5 and y2 = -45
now sub
slope(m) = (-45 - (-21) / (5 - 2)
slope(m) = (-45 + 21) / 3
slope(m) = -24/3
slope(m) = - 8

with me so far ?

Answer 9

let me know and I will continue

Answer 10

you know the first coordinate is x and the second is y , right?

Answer 11

yes...first one is x and second one is y

Answer 12

P0stir0n@ Yes

Answer 13

texaschic101@ sorry I don't understand

Answer 14

where are you getting lost

Answer 15

(2,-21)
| |
x y

Answer 16

texaschic101 @ I jut completely get lot front he beginning of what you wrote

Answer 17

P0sitr0n @ Yes I know that

Answer 18

you are given 2 sets of numbers...set 1 and set 2
label your numbers...set 1 = (x1,y1)....so (2,-21) : x1 = 2 and y1 = -21
set 2 ....(x2,y2) ... (5,-45)...x2 = 5 and y2 = -45
do you understand this

Answer 19

texaschic101 @ yes. i understand

Answer 20

now to find the equation, we first need to find the slope. We will use the slope formula for this.
slope(m) = (y2 - y1) / (x2 - x1)
(2,-21)..x1 = 2 and y1 = -21
(5,-45)..x2 = 5 and y2 = -45
now we sub this into our formula
slope(m) = (-45 - (-21) / (5 - 2)
slope(m) = (-45 + 21) / 3
slope(m) = -24/3
slope(m) = -8

any questions ? Any at all ?

Answer 21

this is not the answer...there is more. I just want to make sure you are understand ing what I am doing. Do you understand ?

Answer 22

I think I understand

Answer 23

Now we will continue..
Now you can use the formula jdoe posted up there, but I prefer to just use y = mx + b formula.

y = mx + b
slope(m) = -8
you can use either of your points...I will use (2,-21)..x = 2 and y = -21
now we sub
-21 = -8(2) + b
-21 = -16 + b
-21 + 16 = b
- 5 = b

so our slope(m) = -8 and our y intercept (b) = -5....so our equation is :
y = -8x - 5

Any questions ?

Answer 24

texaschic101 @ nope

Answer 25

ok....let me try again

we already found that the slope (m) was -8

now we will use y = mx + b.....we are now looking for b, the y intercept
we sub in our slope(m) = -8
we then pick one of our sets of points...(2,-21)...x = 2 and y = -21
now we sub our stuff into the formula.

y = mx + b -- solve for b, the y intercept
-21 = -8(2) + b
-21 = -16 + b
-21 + 16 = b
- 5 = b

now our slope(m) = -8 and our y intercept(b) = -5
so our equation is : y = -8x - 5

Still lost ?

Answer 26

nope, I understand now, thanks

Answer 27

good to hear :)