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

Answer:

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

Step-by-step explanation:

Given as :

The given equation of one line = y = $\dfrac{-1}{3}$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 = $\dfrac{-1}{3}$

Slope of this line = m = $\dfrac{-1}{3}$

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 = $\dfrac{-1}{m}$

I.e M = $\frac{-1}{\frac{-1}{3}}$

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