Finding the equation

[shawie]

Write an equation of the line through (1, 4) and (5, -2)

the answer is: 3x+2y=11

where does 11 come from?

 

[pka]

Well, 3(1)+2(4)=11 & 3(5)+2(−2)=11.
A line Ax+By=C has slope (−A/B).
So you know where 3x+2y comes from.

 

[arthur ohlsten]

many ways to do this problem. A way is to write the equation of a straight line and substitute values

y = mx+b given : x=1 y=4 and x=5 y=-2
substitute first set of values
eq1 4=m[1]+b substitute second set of values
eq2 -2=m[5]+b two equations in 2 unknowns subtract eq2 from eq1
-----------------
6=m[1-5]
m= -6/4
m=-3/2 substitute into eq1 or eq2 to find b

eq1 4=[-3/2] [1] + b
4+ 3/2 =b
b=11/2

we know m and b then rewrite equation of a straight line
y=mx+b
y=-3/2 x +11/2 answer
to get it into your form multiply both sides by 2
2y=3x+11 or
2y - 3x =11 answer

Arthur

 

[ting]

You could start by finding the equation in slope intercept form.

y = mx + c

Use the two points to find the slope, (y/x)

(-2-4)/(5-1) = -(6/4) = -(3/2)


y = -(3/2)x + c

Substitute one of the points, (1, 4) and solve for, c, the y intercept.


4 = -(3/2) + c


c = (11/2)

Equation is

y = -(3/2)x + (11/2)

Rearrange to Ax + By = C

Multiply through by 2

2y = -3x + 11

Add 3x to both sides.

3x + 2y = 11

 

[arthur ohlsten]

b is where the line crosses the y axis
you have 2 points on the line extend the line and see where it intercepts the y axis at x=0 y=11 if you make no errors
Arthur