Find an equation of the line passing through the pair of poi

Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C. (7,9), (6,-8) .

Solution

We know that the slope-intercept form of the equation of a line is y = mx +c, where m is the slope and c is the y-intercept. Here, m =[ 9-(-8)]/(7-6) = 17. Then, the equation of the line changes to y = 17x +c. Now, since the line passes through the point ( 7,9) , on substituting x = 7 and y= 9 in the equation of the line, we get 9 = 17*7 +c so that c = 9- 119= -110. Then the equation of the line becomes y = 17x -110 or, 17x - y = 110.

We can verify the result by substituting x = 6 and y = -8 in this equation. On substituting, we get 17*6 -(-8) = 110 or, 102+8 = 110, which is correct. Hence the equation of the required line is 17x -y = 110.