Question

Find the equation, in standard form, of the line passing through the points (2,-3) and (4,2).

Answer 1

let us do this step-by-step okay? I will give you hints and you the rest

Answer 2

first, solve for the slope

Answer 3

ok

Answer 4

the slope is 5/2, right?

Answer 5

\[slope=m=\frac{ \Delta y }{ \Delta x }=\frac{ rise }{ run }=\frac{ y_2 - y_1 }{ x_2 - x_1 }\]

Answer 6

Ok, i did that. I did 2-(-3)/ 4-2 and i got 5/2

Answer 7

now that you have the slope, use the point-slope form equation
\[y - y_1 = m(x-x_1)\]

Answer 8

ooh

Answer 9

go head, plug in the numbers

Answer 10

y-2=5/2(x-4)?

Answer 11

use distributive property to multiply the slope into x and -4

Answer 12

y-2=5/2x-10

Answer 13

not 5/2x
it is 5x/2 be very careful

Answer 14

ah

Answer 15

add 2 to both sides?

Answer 16

\[\frac{ 5 }{ 2 } \times \frac{ x }{ 1 } = \frac{ 5x }{ 2 }\]

Answer 17

then solve for y
you can achieve this by isolating y and in your problem you need to add 2 on both sides of the equation (left and and right hand sides)

Answer 18

and that's the answer in standard form? y=5x/2-8?

Answer 19

nope that is the slope form

Answer 20

standard form is
\[Ax+By=C\]

Answer 21

so would it be 5x+2y=8?

Answer 22

how so?

Answer 23

because the 5 is next to x, the -8 is constant and 2 is what's left i guess? and i'm not sure if they can be negative

Answer 24

first, rearrange it in the format of
Ax + By = C
the coefficient of x is 5/2
the coefficient of y is 1
and C = 8
rearranging
\[y = \frac{ 5 }{ 2 }x - 8\]
add 8 to both sides
subtract y to both sides
then make sure that everything is in whole number

Answer 25

always make sure that A is a positive integer

Answer 26

ok, so is it 5x-2y=16?

Answer 27

yes

Answer 28

yay, thank you so much :)!