Question

Find the slop of the line perpendicular to the line y=(1/3)x - 7?

Answer 1

Question:

Find the slope of the line perpendicular to the line y = (1/3)•x - 7.

Answer:

The slope of the perpendicular line to the given line is (-3) .

Note:

• The slope, y-intercept form of a straight line is given by; y = mx + c ,

where "m" is the slope and "c" is the y-intercept of the straight line.

• Geometrically ,the slope of a line is the tangent of the angle which the line makes with the positive x-axis measured in anti-clockwise direction.

• Slope of a line is generally denoted by "m" and it is given by ; m = tan@ ,

where, @ is the angle which the line makes with the positive x-axis measured in anti-clockwise direction.

• Slope of a straight line is also given

by, m = ∆y/∆x = (y2 - y1)/(x2 - x1)

where, (x1,y1) and (x2,y2) are the coordinates of the points lying on the line.

• Let L1 and L2 be two straight lines with the slopes m1 and m2 respectively,

Then ,

1) The lines L1 and L2 are parallel , if ;

m1 = m2

2) The lines L1 and L2 are perpendicular, if ; m1•m2 = -1

Solution:

Here,

The given equation of the straight line

is ; y = (1/3)•x - 7

Clearly,

On comparing the given equation of the straight line {y = (1/3)•x - 7} with the slope, y-intercept form of the straight line,

We get,

Slope of the given line is 1/3 .

Let the slope of the given line be m1 .

Thus , m1 = 1/3

Now,

Let the slope of the perpendicular line to the given line be m2.

Also,

We know that,

If two straight lines are parallel, then the product of their slopes must be equal to -1 .

Thus,

=> m1•m2 = -1

=> (1/3)•m2 = -1

=> m2 = -3

Hence,

The slope of the perpendicular line to the given line is (-3) .