How do you write an equation of a line given (-1, 2) and (3, -4)?

2 Answers
Oct 17, 2017

3x+2y+1=0

Explanation:

Standard form of equation with two points given is
yy1y2y1=xx1x2x1
y(4)2(4)=x313

y+46=x34
4y16=6x18

6x+4y=2
3x+2y=1

Oct 17, 2017

y=32x+12

Explanation:

Okay so there are 3 main forms you can use:
- slope-intercept form [y=mx+b]
- standard form [Ax+By=C]
- point-slope form [y1y2=m(x1x2)]

Since you did not specify which form you wanted it in, I am going to use slope-intercept form because that's the easiest to understand, in my opinion. (:

y=mx+b

SLOPE (m)
To find m (slope), you need to find riserun, or which is the change in y divided by the change in x. Use this formula: y1y2x1x2
(1,2)=(x1,y1)
(3,4)=(x2,y2)

It doesn't matter which coordinate pair you choose to be (x1,y1) or (x2,y2). Just stay consistent!

m=2(4)13=2+413=64=32
m= -3/2#

Y-INTERCEPT (b)
Choose one of the coordinates to substitute into y=mx+b, which will be substituting for x and y.
I chose (1,2). Substitute m for 32.
(2)=(32)(1)+b
Solve for b.
2=32+b
b=12

FINAL FORM
Substitute m and b for their values. This is your answer!
y=32x+12