Find an equation of the line that passes through the points

Find an equation of the line that passes through the points. (4,2) and (5,8) y = - 6x - 22 y = 6x - 22 y = -6x+ 22 y - 22 y = 6x

Solution

Let the equation of the line be y = mx +c where m is the slope and c is the y-intercept. Since the line passes through the point ( 4, 2), on substituting these values of (x, y) in the above equation, we have 2 = 4m + c...(1)

Also, Since the line passes through the point ( 5, 8), on substituting these values of (x, y) in the above equation, we have 8 = 5m + c...(2)

From these two equations, we have c = 2 - 4m = 8 - 5m Therefore 5m - 4m = 8 - 2 or, m = 6. On substituting this value of m in the 1st equation, we have 2 = 4(6) + c or, 2 = 24 + c or, c = 2 -24 = -22. Thus the equation of the required line is y = 6x - 22. We can verify this by substituting the values of m and c in the 2nd equation. On substitution, we get 8 = 5(6) + ( -22) or, 8 = 30 -22 which is correct.