Question

Write a slope-intercept equation for a line passing through the point (4,-2) that is parallel to the line 4x+7y=9. Then write a second equation for a line passing through the point (4,-2) that is perpendicular to the line 4x+7y=9.The equation of the parallel line is[____]The equation of the perpendicular line is [____]

Answer 1

a) P1 = (4, -2)

Parallel 4x + 7y = 9

1.- Find the slope of the parallel line

7y = -4x + 9

y = -4x/7 + 9/7

slope = m = -4/7

2.- Find the equation of the line

y - y1 = m(x - x1)

y + 2 = -4/7(x + 4)

3. Simplifying

y = -4x/7 - 16/7 - 2

4.- Result

y = -4x/7 - 30/7 This is the parallel line

b) Perpendicular

slope = m = 7/4

1.- Equation of the line

y + 2 = 7/4(x - 4)

2.- Simplifying

y + 2 = 7x/4 - 7

y = 7x/4 - 7 - 2

3.- Result

y = 7x/4 - 9 This is the perpendicular line