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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation of a line through (x1 , y1) and (x2 , y2) is

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

For the points (-2,4) and (3, -5).

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

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

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

=> 9x + 5y - 2 = 0

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

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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)

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