Question

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

Answer 1

Answer:

Step-by-step 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

$a=\frac{2-(-1)}{-2-3} =\frac{2+1}{-5} =-\frac{3}{5}$

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 $(x_{0},y_{0}) , (x_{1},y_{1}) ,x_{0}\neq x_{1}$

Here is: $\frac{x-x_{0} }{x_{1}-x_{0} } = \frac{y-y_{0} }{y_{1}-y_{0} }$

Then, we can write for this case:

$\frac{x-(-2)}{3-(-2)} =\frac{y-2}{-1-2} \\\frac{x+2}{5} =\frac{y-2}{-3} \\-3(x+2) = 5( y-2)\\-3x-6=5y-10\\3x+5y-4=0\\or\\y=-\frac{3}{5}x+\frac{4}{3}$

P.S: You type wrongly the signs?