# Write down the equation of the line that passes through the point (-2,4) and (3, -5).

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### 3 Answers

The equation between two points ( x1, y1) and ( x2 , y2) is given by ( y- y1) = [ ( y2 - y1) / (x2 - x1)]*(x - x1)

Now we have the points (-2,4) and (3,-5)

Substituting the values we get:

y - 4 = [ ( -5 - 4)/ (3 + 2)](x + 2)

=> y - 4 = (-9 / 5) ( x + 2)

=> 5(y - 4) = -9(x +2)

=> 5y - 20 = -9x - 18

=> 9x + 5y - 2 = 0

**The required equation of the line is 9x + 5y - 2 = 0.**

The equation of the line passing through (x1,y1) and (x2,y2) is given by:

y-y1 = {y2-y1)/(x2-x1)}(x-x1).

Therefore the equation of the line passing through the points (-2,4) and (3;-5) is given by:

y-4 = {(-5-4)/(3-(-2))}(x-(-2))

y-4 = (-9/5)(x+2)

5(y-4)= -9(x+2) = -9x-18.

5-20+9x+18 = 0.

9x+5y -2 = 0.

Therefore the equation of the line passing through the points (-2,4) and (3;-5) is 9x+5y-2 = 0.

We'll write the equation of a line when knowing 2 points:

(y2 - y1)/(y - y1) = (x2 - x1)/(x - x1)

We'll identify the coordinates of the 2 points:

x1 = -2, x2 = 3, y1 = 4, y2 = -5

We'll substitute them in the equation above:

(-5-4)/(y-4) = (3 - (-2))/(x - (-2))

-9/(y-4) = 5/(x + 2)

We'll cross multiply:

5(y - 4) = -9(x+2)

We'll divide by 5:

(y - 4) = (-9/5)*(x+2)

**The equation of the line that passes through the given points is:**

**(y - 4) = (-9/5)*(x+2)**