find an equation of the line containing the given pair of points (2,1) and (6,4)?

Question

find an equation of the line containing the given pair of points (2,1) and (6,4)

Again working with my son on algebra problems and have not been able to get this one. He has it done I just dont know if it is right, lol. Can someone help?

What is the equation of the line?

Answer 1

m = (4 - 1) / (6 - 2) = 3 / 4 is slope (gradient)
Passes thro`(2,1)
Equation of line of slope m passing thro` (a,b) is:-
y - b = m (x - a)
y - 1 = (3 / 4) (x - 2)
y = (3 / 4) x - 6 / 4 + 1
y = (3 / 4) x - 1 / 2

Answer 2

it is simple.. you do not need to remeber anything except this..

write down the equation of a line which could look like

y = mx + c, m is slope and c is a constant which we don't know right now

since this line has to go through both the points (2, 1) and (6,4)

let us see.. (2,1) will lie on y = mx + c, so the point should satisfy the equation when you substitute x =2 and y = 1

so lets do that... then we get an equation => 1 = 2m + c

so 2m+ c = 1 ...........equation(a) so c = 1-2m

now let us repeat the same with the 2nd point (6,4) also.. ok..

so hen 4 = 6m + c ..... equation (b)

let us substitute c = 1-2m in equation (b) .. ok

so, 4 = 6m + 1 - 2m => 4 - 1 = 4m => m = 3/4

good we got m = 3/4 , so substitute this into c = 1-2m

ok. then we will get c = 1-2*3/4 = 1-3/2 = -1/2

so the equation will be , y = 3/4x -1/2

or we can simplify it by multiplying with 4 both sides ok

then it will be 4y = 3x - 2
answer... this equation qill contain both the given points.. and it will satisfy both the points..
ok..

Answer 3

Okay hold on..

First of all we must find out the slope of these points. The equation for slope is..
y2-y1 over x2-x1

So we know that in a point the first number is the x coordinate and the second number is the y coordinate. Personally I like to label my coordinates so I don't get confused when I plug them into the equation.

So in (2,1) x1=2 and y1=1
And in (6,4) x2=6 and y2=4

So let's plug them into the equation.

4-1 / 6-2
3/4 <-- So that's your slope. Youc an't simplify it anymore because it's already simplified.

Now that you got your slope, you need to write your equation. So we use the point-intercept equation. Which is
y-y1=m(x-x1) In which m= the slope.
So let's plug in our coordinates and slope.

y-y1=m(x-x1)
y-1=3/4(x-2) Do distributive property.
y-1=3/4x-6/4 Now we simplify 6/4
y-1=3/4x-3/2 That's your equation

That could be your equation but if it's specified to put into standard form (ax+by=c) or slope intercept form (y=mx+b) you have to convert it, or else the equation will be incorrect. Since it wasn't specified your equation is y-1=3/4x-3/2 .

Hope I helped!

Answer 4

You gotta use the rise over run thing.

The first digits in each pair are the x-input, and the second are the y-input.

Take the y-inputs and subtract them from one another. 4-1=3 So that would be the rise.

Do the same with the x-inputs. 6-2=4.
That is the run.

So rise over run (in fraction form) is 3/4. That's the slope (m) of the line.
The equation formula is y=mx+b
So input your information (from either coordinate pair) to find out the entire equation.

Let's use the second one so we can use pretty much all whole numbers.

y=mx+b
4=3/4(6)+b

So I dunno if this is making sense, but it's right.
So first multiply the mx
3/4(6)=8

So 4=8+b
And 4-8=-4
So b=-4

So the equation of the line is y=3/4x-4.

P.S. You ARE an angel. You're helping your child. :]

Answer 5

Equation of a straight line passing through two points (x1,y1) and (x2,y2) is
(y-y1)/(x-x1) = (y2-y1)/(x2-x1). This formula is derived based on the property of the right triangles formed using these points.

Using this formula for the points in this problem,
(y-1)/(x-2) = (4-1)/(6-2) = 3/4

4y-4 = 3x-6
4y = 3x-2 or 4y-3x+2 = 0.

To check if this equation is correct, substitute the two points in the equation and see if the points satisfy the equation.

Answer 6

First we need to find the slope:

4-1/ 6-2 = 3/4

So the slope is 3/4.

Now, we have the equation y=3x/4 +1
or it could also be y=3x/4 +4
Because we can plug in any y intercept.

Am I the only one who gets annoyed when someone posts "okay hold on" so they can be the first poster, while everyone else has the answer done already, and then they edit the "okay hold on" to put the right answer? lol just thought i would vent

Answer 7

find the slope first
4-1/6-2= 3/4

then find y intercept
1=2(3/4)+b
1= 6/4+b
-1/2=b

so y=3/4x-1/2

Answer 8

4-1/6-2=3/4
(1-y)=3/4(2-x) would be the ansey in splope-intercept form. Glad to help, if you have any more algebra questions just ask

Answer 9

y-(-3)/x-(-a million)=y-(-9)/x-(-5)= y+3/x+a million=y+9/x+5 (y+3)(x+5)=(x+a million)(y+9) slope =m= y2-y1/x2-x1=(-9)-(-3)/(-5)-(-a million)=-9+3/-5+... or=a million.5 y=mx+b y=a million.5x+b if x =0 y=b (y+3)(x+5)=(x+a million)(y+9) or (y+3)(0.5)=(0+a million)(y+9) =5(y+3)=y+9 5y+15=y+9 or 4y=-6 y=--a million.5 y=mx+b y=a million.5x -a million.5

Answer 10

(change in) y / (change in) x = 4-1/6-2 = 3/4 = slope
y= 3/4 x + b
1 = 3/4 (2) + b
1 = 1 1/2 +b
1 - 1.5 = 1.5-1.5 + b
-0.5=b

final equation:
y = 3/4 x - 0.5