How do you find the equation of line L that passes through the points (1,3) and (-3,4)?

Question

11973 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-06T14:20:13

The answer is: $y=-1/4x+13/4$ .

It is possible to use this formula, that is the formula to find a line given two points $A(x_A,y_A)$ and $B(x_B,y_B)$ :

$(y-y_A)/(y_B-y_A)=(x-x_A)/(x_B-x_A)$ .

So:

$(y-3)/(4-3)=(x-1)/(-3-1)rArry-3=-1/4(x-1)rArr$

$y=-1/4x+1/4+3rArry=-1/4x+13/4$ .

Answer 2 · 2015-02-07T03:12:16

I created a video that answers the question and shows you how to check you work.
http://www.frontporchmath.com/topic/equation-of-a-line-question-1/

To solve this problem you first find the slope of the line, using the two points $(1,3)$ and $(-3,4)$ .

$(Delta y)/(Delta x) = (4 - 3)/(-3 - 1) = -1/4$

Then you use the y-intercept equation of a line using the slope above and one of the above sets of points to find the y-intercept.

$y = mx + b$
$4 = -1/4(-3) + b$
$4 = 3/4 + b$
$3 1/4 = b$

Then just plug that information into $y=mx+b$

$y= -1/4x +3 1/4$
or
$y=1/4x +(13)/4$