Question

Can someone walk me through the process of solving this question. Attachment below. :) MEDAL+FAN

Answer 1

Step 1: solve for slope intercept (y=mx+b) form.
This form is nice because it has the slope in it easy to find.

Can you do that?

Answer 2

Thank you and yes. I will post my slope when I am done solving for it :)

Answer 3

2/5 is the slope I got. Is that correct..... slope from 2x-5y=2

Answer 4

Yup, that's right.
Step 2: Find the slope of the perpendicular line
To do this, find the negative reciprocal of the original slope. (The negative reciprocal of a/b is -b/a)

Answer 5

Then, use your new slope (-5/2) and the point you were given in the problem (-3,1).
Plug these into the point-slope equation:
(y-y₁) = m(x-x₁)

Then, you can solve for standard form:
Ax + By = C

Answer 6

in case you don't understand negative reciprocal, it means flip the fraction and then make it negative. you have the slope 2/5.... flip it upside down, then make it negative.

that will be the slope of the perpendicular line

Answer 7

Thank you @phi for extra information

Answer 8

so..... I have this:

Answer 9

yes, now you have to rearrange it into standard form to match one of the choices

Answer 10

ohhhh okay

Answer 11

My first thought is multiply both sides by 2 (this will get rid of the fraction)

Answer 12

but shouldnt i distribute the fraction to the (x+3)?

Answer 13

you could, (there are many ways to do it)... but multiply both sides of the equation by 2 is simpler

Answer 14

wellll I think I messed up. I will post my work in a second

Answer 15

that looks fine, but standard form does not have fractions (or a negative number times the x)

so now multiply both sides (all terms) by 2

Answer 16

\[ 2\left(\frac{5}{2} x + y\right) = 2 \cdot -6.5 \]
and simplify

Answer 17

you get
5x + 2y = -13

Answer 18

another way to do this is start with
(y-1) = -5/2 (x + 3)
multiply by 2 both sides
2(y-1) = -5(x+3)
distribute (on both sides)
2y - 2 = -5x -15
move the -5x to the left side... add +5x to both sides
5x+2y -2 = -5x+5x -15 or
5x + 2y -2 = -15
add +2 to both sides
5x+2y= -13

Answer 19

ohhh ok I see

Answer 20

THANK YOU SO MUCH!!!!! BOTH OF YOU GUYS! I REALLY APPRECIATE IT AND WISH I COULD GIVE METALS TO BOTH OF YOU.!!!