Find the equation of a line that is parallel to the line y

Find the equation of a line that is parallel to the line y = - 19x and contains the point (1, -6). (Type your answer in slope-intercept form.)

Solution

Let the equation of the desired line be y = mx + c, where m is the slope of the line and c is the y-intercept. Since this line is parallel to the line y = - 19x, the slope of the desired line has to be same as that of y = - 19x. Thus, m = -19. Then the equation of the desired line changes to y = -19x + c. Since this line passes through the point (1, - 6), on substituting these values of (x, y) in the line\'s equation, we get - 6 = - 19 + c . Therefore, c = 19 - 6 = 13. Then, the equation of the desired line is y = - 19x + 13