Respuesta :
The first step to solve this problem is arrange the equation in the standard line equation form, which is given below:
[tex]y\text{ = m}\cdot x\text{ + }b[/tex]y = m*x + b
Where "m" is the slope of the line and "b" is the constant shift. To find the perpendicular line we need to find a line with the slope as shown below:
[tex]m_1\text{ =-}\frac{1}{m}\text{ }[/tex]m1 = -1/m
We need to arrange the given expression.
[tex]\begin{gathered} 5x\text{ + 3y = 7} \\ 3y\text{ = 7 - 5x} \\ y\text{ = -}\frac{5}{3}x\text{ + }\frac{7}{3} \end{gathered}[/tex]5x + 3y = 7
3y = 7 - 5x
y = (-5/3)x + 7/3
The slope of the given line is -5/3 to find the perpendicular line we need to find the slope -1/m. Which is done below:
m1 = -1/(-5/3) = -1*(-3/5) = 3/5
The perpendicular line we want has the a slope of 3/5. We can find the constant shift by applying the given point.
Perpendicular:
y = (3/5)*x + b
Applying the point:
3 = (3/5)*2 + b
3 = 6/5 + b
b = 3 - 6/5 = 15/5 - 6/5 = 9/5
Therefore the perpendicular line is given by:
y = (3/5)*x + 9/5
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