Question

What is the equation of the line that passes through the points (-1, 3) and (1, 11)?

Answer 1

4x - y = 1

4x + y = 1

x - 4y = -13

4x - y = -7

Answer 2

@ganeshie8

Answer 3

you may do it two ways :
1) plugin points in each options and check which one satisfies both points
2) find the slope, and find the equation of line.

Answer 4

pick one ?

Answer 5

Lets do 1

Answer 6

plugin (-1, 3) in first option :

4x - y = 1
4(-1) - 3 = 1
-4 - 3 = 1
-7 = 1

which is FALSE. so option 1 doesnt satisfy

Answer 7

check if option2 satisfies..

Answer 8

ok

Answer 9

can u help me please?

Answer 10

@ganeshie8 showed you the one way, I'll show you the other he proposed:

Find slope of line between two points \((x_1,y_1)\) and \((x_2,y_2)\):

\[m = \frac{y_2-y_1}{x_2-x_1} = \frac{11-3}{1-(-1)} = \frac{8}{2} = 4\]We know our line will be one with slope \(m=4\) which is enough information to discard half of the possible answers.

Next, use the point-slope equation to find the full equation of the line given its slope and a known point \((x_0,y_0)\):

\[y-y_0=m(x-x_0)\]Plug in the value we found for \(m\) and either of the two known points. Now you have the equation of the line. You may have to rearrange it to match one of the answer choices.

For this particular problem, it might be faster to simply go down the list testing possible answers, but you really should know how to find the equation of the line from two points, because many times you'll have to do this without the benefit of being able to choose from a menu of answers!

Answer 11

I still dont really know the answer though....

Answer 12

is it x - 4y = -13?

Answer 13

okay simply find the gradient first, because you want to complete the equation y=mx+c

the gradient can be found by using the x and ys of both points as shown:
y1-y2/x1-x2 (rise/run)

which is (-1)-(1)/(3)-(11) because gradient is basically the difference.
gradient is 'm' in the equation 'y=mx+c'
hence we have part complete - 'y=0.25x+c'

to find c, the constant, sub in the x and y from either point. I'll use the (1,11) one.
y=mx+c
11=0.25(1)+c
c=11-0.25
c=10.75

all thats needed now is to reformat the equation so it looks:
y=0.25x+10.75

There you got it, your equation of line!

Answer 14

so it is x - 4y = -13???
the last one?

Answer 15

the equation of line is what your equation looks like without the x and y as numerals.

this is so you can sub in any point in the line and get the same answer to plot a line.

so the FORMAT for your equation has to be a variation of 'y=mx+c'
where only the m and c are filled up. examples are:

y=14x+10
y=25x+18
y=-10x-8
y=3x

those are how equation of lines look like.

Answer 16

wait dammit the method was correct but i swapped the y and x by accident. just swap it over on the gradient.

Answer 17

so 4x-y=-7

Answer 18

Yes, that is correct! @naturegirl

Answer 19

yeah should be

Answer 20

thanks to everyone who helped me!

Answer 21

Testing:
\[4(-1)-(3) = -7\]\[-4-3=-7\checkmark\]
\[4(1)-(11) = -7\]\[4-11=-7\checkmark\]