Write an equation for the line that goes through the points

Write an equation for the line that goes through the points (2,5) and (-1,8).

Solution

Let the equation of the line be y = mx + c. Since it goes through the points (2, 5) and ( - 1, 8), on substituting these values of x and y in the line\'s equation, we have,

5 = 2m + c or, c = 5 - 2m and 8 = -m + c or, c = 8 + m. On equating these 2 values of c , we get 5 - 2m = 8 + m or, 3m = 5 - 8 = -3 so that m = -1. Now, c = 5 - 2m = 5-2(-1) = 5 + 2 + 7. Thus the equation of the line that passes through (2, 5) and ( - 1, 8) is y = -x + 7