Question

Find an equation of the line that satisfies the given conditions.

Through (8, 5); perpendicular to the line y = 9

Answer 1

The equation of line passing through points ( 8 ,5 ) and perpendicular to given line equation is y = 5 .

Explanation:

Given as :

The equation of line is y = 9

The standard equation of line is written as

y = m x + c , where m is the slope of line and c is the y-intercept

Now, comparing the given line equation with standard line equation

I.e y = 0 × x + 9

So, slope of given line = m = 0

Now, another line is passing through the point ( 8 , 5 ) and is perpendicular to the given line equation

So, The equation of another line is

y = M x + c

where M is the slope

∵ both lines are perpendicular

So, the products of lines = m × M = - 1

I.e 0 × M = - 1

Or, M = 0

Now, equation of another line passing through points ( 8 ,5 ) and slope 0 is

y = M x + c

I.e 5 = 0 × 8 + c

Or, 5 = c

So, The equation of another line is

y = 0 × x + 5

I.e y = 5

Hence The equation of line passing through points ( 8 ,5 ) and perpendicular to given line equation is y = 5 . Answer

Answer 2

`x=8`

Explanation:

Given:

The equation of the given line is
`y=9`

A point on the unknown line is (8, 5).

The unknown line is perpendicular to the line
`y=9`.

A line of the form
`y=a` where 'a' is a constant is a line parallel to the x axis. The line has a constant value for 'y' irrespective of the value of 'x'. The slope of such lines are equal to 0. So, slope of the known line is 0.

Now, when two lines are perpendicular, the product of their slopes is -1.

Let the slope of the unknown line be 'm', then:

`m* 0 =-1\\m=-(-1)/(0)=` undefined.

Therefore, the slope of the unknown line is undefined. A line parallel to y axis has undefined slope. So, the equation of the unknown line is of the form:

`x=b` where, 'b' is a constant and is equal to the abscissa (x value) of the line.

As per question, (8, 5) lies on this line. Therefore, the value of 'x' is 8.

So, the equation of the unknown line is
`x=8`