# Math Help - [SOLVED] Find the equation of a line through two points.

1. ## [SOLVED] Find the equation of a line through two points.

Hi
I need to work out the equation, something like Y=3X, for the line that goes through these two points on a graph: (1,4) and (2,3)
Minds gone blank!
Thanks kindly.

2. General solution. Equation of a line passing tru point (a,b) and (c,d):

$\frac{x-a}{a-c}=\frac{y-b}{b-d}
$

Solve for y. The order of a,b,c,d is important.

-O

3. Don't know what I'm doing wrong...
If a=1, b=4, c=2 and d=3

Then I get x=y-4 which isn't right.

"solve for y" is confusing me.

4. a=1, b=4, c=2 and d=3
$
\frac{x-a}{a-c}=\frac{y-b}{b-d} \rightarrow
\frac{x-1}{1-2}=\frac{y-4}{4-3} \rightarrow
\frac{x-1}{-1}=\frac{y-4}{1} \rightarrow
-x+1=y-4
$

Gives:
$
y=-x+5
$

-O

Hi
I need to work out the equation, something like Y=3X, for the line that goes through these two points on a graph: (1,4) and (2,3)
Minds gone blank!
Thanks kindly.
"Something like Y= 3X" would pass through (0,0). It would be better to use the more general y= mx+ b which works for every non-vertical line. Since the line passes through (1, 4), x= 1, y= 4 satisfy the equation: 4= m(1)+ b or m+ b= 4. Since the line passes through (2, 3), x= 2, y= 3 satisfy the equation: 3= m(2)+ b or 2m+ b= 3. You can solve those two equations for m and b and so get the equation.