Find an equation of the line that passes through the point 2

Find an equation of the line that passes through the point (-2,4) and is parallel to the line 2x-4y-8=0

Solution

The equation of the line 2x- 4y - 8 = 0 can be changed to its slope intercept form as under:

2x - 4y - 8=0 or, 4y = 2x - 8 or, y = (1/2)x - 2 ...(1)

Let the equation of the required line be y = mx + c where m is the slope and c is the y-intecept. Since this line is parallel to the given line, the slopes of the two lines must be same. Therefore, m = 1/2. Then the equation of the required line changes to y = (1/2)x + c. Since this line passes through ( -2 , 4), on substituting these values of x and y in the equation of the line, we have, 4 = (1/2)( -2) + c or, c -1 = 4. Therefore, c = 4 + 1 = 5. Then the equation of the desired line is y = (1/2)x + 5 .In standard form, the equation is 2y = x + 10 or, 2y -x -10 = 0.