Question

Through (1,3) perpendicular to 3x+2y=5

Answer 1

Answer:

The equation of line passing through points (1 , 3) and perpendicular to given line is  y = $\dfrac{2}{3}$ x + $\dfrac{7}{3}$

Step-by-step explanation:

Given as :

The equation of line is 3 x + 2 y = 5

Or , 2 y = - 3 x + 5

Or , y = $\dfrac{-3}{2}$ x + $\dfrac{5}{2}$

Another line is passing through point (1 , 3) and perpendicular to given line equation

Now, From standard line equation

i.e y = m x + c

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

Now, comparing the given line equation with standard line equation

i.e y = $\dfrac{-3}{2}$ x + $\dfrac{5}{2}$

So, The slope of line = m =  $\dfrac{-3}{2}$

According to question

Another line is perpendicular to the given line

So, for perpendicular property, The product of the lines = - 1

Let the sloe of another line = M

So, m × M = - 1

∴ M = $\dfrac{-1}{m}$

Or. M = $\frac{-1}{\frac{-3}{2}}$

I.e M = $\dfrac{2}{3}$

So, the slope of another line = M = $\dfrac{2}{3}$

Now, equation of line passing through slope M and point (1 , 3)

I.e equation of line in slope-points

So, y - $y_1$ = m ( x - $x_1$ )

or, y - 3 = ( $\dfrac{2}{3}$) × ( x - 1 )

Or, 3 × (y - 3) = 2 × (x - 1)

Or, 3 y - 9 = 2 x - 2

Or, 3 y = 2 x - 2 + 9

Or, 3 y = 2 x + 7

∴ y = $\dfrac{2}{3}$ x + $\dfrac{7}{3}$

So, The equation = y = $\dfrac{2}{3}$ x + $\dfrac{7}{3}$

Hence, The equation of line passing through points (1 , 3) and perpendicular to given line is  y = $\dfrac{2}{3}$ x + $\dfrac{7}{3}$  Answer