Respuesta :
Answer:
The equation of line passing through points (1 , 3) and perpendicular to given line is y = [tex]\dfrac{2}{3}[/tex] x + [tex]\dfrac{7}{3}[/tex]
Step-by-step explanation:
Given as :
The equation of line is 3 x + 2 y = 5
Or , 2 y = - 3 x + 5
Or , y = [tex]\dfrac{-3}{2}[/tex] x + [tex]\dfrac{5}{2}[/tex]
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 = [tex]\dfrac{-3}{2}[/tex] x + [tex]\dfrac{5}{2}[/tex]
So, The slope of line = m = [tex]\dfrac{-3}{2}[/tex]
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 = [tex]\dfrac{-1}{m}[/tex]
Or. M = [tex]\frac{-1}{\frac{-3}{2}}[/tex]
I.e M = [tex]\dfrac{2}{3}[/tex]
So, the slope of another line = M = [tex]\dfrac{2}{3}[/tex]
Now, equation of line passing through slope M and point (1 , 3)
I.e equation of line in slope-points
So, y - [tex]y_1[/tex] = m ( x - [tex]x_1[/tex] )
or, y - 3 = ( [tex]\dfrac{2}{3}[/tex]) × ( 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 = [tex]\dfrac{2}{3}[/tex] x + [tex]\dfrac{7}{3}[/tex]
So, The equation = y = [tex]\dfrac{2}{3}[/tex] x + [tex]\dfrac{7}{3}[/tex]
Hence, The equation of line passing through points (1 , 3) and perpendicular to given line is y = [tex]\dfrac{2}{3}[/tex] x + [tex]\dfrac{7}{3}[/tex] Answer
