What is the slope of a line that is perpindicular to the line whose equation is 3x plus 4y equals 12?

Answer 1

3x + 4y = 12 can be written as 4y = -3x + 12 , which can be simplified to, y = -3/4x + 3

The slope of this line is the coefficient of x, namely, -3/4.

When two straight lines are perpendicular then the product of their slopes/gradients is -1.

Therefore , any line perpendicular to y = -3/4x + 3 has the slope 4/3.

Now select any point on the original line where you wish to create the perpendicular line. Let the coordinates of this point be (a, b).

The general slope/intercept form of equation for a straight line is y = mx + c. Substituting the values of the ordered pair gives : b = 4/3a + c

The two lines intersect at (a, b) and at that point, -3/4x + 3 = 4/3x + c

Then, -3/4a + 3 = 4/3a + c : c = -25/12a + 3

The equation of the perpendicular line is thus : y = 4/3x - 25/12a + 3