Question

The line 4x - 3y + 12 = 0 meets x-axis at A.
Write the co-ordinates of A.
Determine the equation of the line through A
and perpendicular to 4x – 3y + 12 = 0.​

Answer 1

Answer:

For the point A(the point on the x-axis) the value of y=0

4x - 3y +12 = 0

=4x = -12

=x = -3

Co-ordinates of point A are (-3, 0). Here,

(x1, y1)= (-3, 0).

The line given is 4x - 3y +12 =0

3y = 4x + 12

y = 4/3x + 4

slope of this line = 4/3.

therefore, slope of a line perpendicular to given line = -1/4/3 = -3/4.

required equation of the line passing through A is y - y1 = m (x - x1)

y - 0 = -3/4 (x +3)

4y = -3x - 9

3x +4y + 9=0.