Question

write the equation of the line that is perpendicular to the given line and that passes through the given point. y = -1/3x+5;(4,3)

Answer 1

The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9 .

Explanation:

Given as :

The given equation of one line = y =
`(-1)/(3)`x + 5

∵ Equation of line in slope-intercept form is written as

y = m x + c

where m is the slope of line

And c is the intercept of y

Now, Comparing given line equation with standard slope intercept line equation

∴ m =
`(-1)/(3)`

Slope of this line = m =
`(-1)/(3)`

Now, another line is perpendicular to the given line

For perpendicular lines , the products of slope of lines = - 1

Let the slope of another line = M

So, from perpendicular lines condition

m × M = - 1

∴ M =
`(-1)/(m)`

I.e M =
`(-1)/((-1)/(3))`

So, M = 3

∴ The slope of other line = M = 3 , and the line passing through point (4,3)

Now, Again

The equation of line in slope-intercept form

I.e y = M x + c

Now, satisfying the points on line

So, 3 = 3 × 4 + c

Or, 3 = 12 + c

∴ c = 3 - 12

i.e c = - 9

or, The other line equation = y = 3 x - 9

Hence, The equation of line perpendicular to given line equation and passing through point (4,3) is y = 3 x - 9 . Answer