Line that passing to to points.Determine the equation using the points (2,3) and (5,8).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation of a line passing through two points (x1, y1) and(x2, y2) is (x - x1)/(y - y1) = (x2 - x1)/(y2 - y1)

The points we have here are (2,3) and (5,8).

Substituting the given values, we get

(x - 2)/(y - 3) = (5 - 2)/(8 - 3)

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

=> 5x - 10 = 3y - 9

=> 5x - 3y - 1 = 0

The required equation is 5x - 3y - 1 = 0

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write the formula that gives the equation of the line that passing through 2 given points is:

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

We'll identify x1 = 2, x2 = 5, y1 = 3 , y2 = 8.

We'll substitute them into the formula:

(5 - 2)/(x - 2) = (8 - 3)/(y - 3)

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

We'll cross multiply:

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

We'll remove the brackets:

5x - 10 = 3y - 9

We'll move 3y to the left side and we'll move the rest of the terms to the right side:

3y = 5x - 10 + 9

3y = 5x - 1

We'll divide by 3:

y = 5x/3 - 1/3

The equation of the line that passing through the points (2,3) and (5,8) is put in the point slope form and it is:

y = 5x/3 - 1/3

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