Question

What is the equation of the line passing through the points (-2, 2) and (3,-1)?

A.
5
y=--x+ -
3 3
4
B.
C.
y = x-4
3 4
y=-*+-
5 5
D
y = -3x + 8

Answer 1

Explanation:

+ Because of " the line passing through the points (-2, 2) and (3,-1)", that means this line has its equation y = ax + b where

`a=(2-(-1))/(-2-3) =(2+1)/(-5) =-(3)/(5)`

So we write its equation: y = -3/5 x + b.

+ Then, now, we replace x = -2 and y = 2 into y = -3/5 x + b for finding b like:

2 = -3/5 * (-2) + b or 2 = 6/5 + b

so b = 2 - 6/5 = 4/5.

And this line has its equation: y = -3/5 x + 4/5.

Mẹthod 2:

we have a formule for a line that passes 2 points
`(x_(0),y_(0)) , (x_(1),y_(1)) ,x_(0)\\eq x_(1)`

Here is:
`(x-x_(0) )/(x_(1)-x_(0) ) = (y-y_(0) )/(y_(1)-y_(0) )`

Then, we can write for this case:

`(x-(-2))/(3-(-2)) =(y-2)/(-1-2) \\(x+2)/(5) =(y-2)/(-3) \\-3(x+2) = 5( y-2)\\-3x-6=5y-10\\3x+5y-4=0\\or\\y=-(3)/(5)x+(4)/(3)`

P.S: You type wrongly the signs?