Respuesta :
Answer:
y = -[tex]\frac{4}{5}[/tex] x + [tex]\frac{27}{5}[/tex] or
5y = -4x + 27
Step-by-step explanation:
To find the equation of a line with points (3,3) and is perpendicular to 5x+5-4y=0
we will follow the steps below:
First find write the equation: 5x+5-4y=0 in standard form y= mx + c and find the slope
5x+5-4y=0
4y = 5x + 5
divide through by 4
4y /4= 5x/4 + 5/4
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{5}{4}[/tex]
comparing the above with y = mx + c
m= [tex]\frac{5}{4}[/tex]
since the equations are perpendicular.
To find the new slope
[tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
[tex]\frac{5}{4}[/tex] [tex]m_{2}[/tex] = -1
multiply both-side of the equation by [tex]\frac{4}{5}[/tex]
[tex]\frac{4}{5}[/tex]× [tex]\frac{5}{4}[/tex] [tex]m_{2}[/tex] = -1 × [tex]\frac{4}{5}[/tex]
[tex]m_{2}[/tex] = -[tex]\frac{4}{5}[/tex]
The slope of our new equation is -[tex]\frac{4}{5}[/tex]
The points are (3,3)
We can now go ahead and form our new equation
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 3 = -[tex]\frac{4}{5}[/tex] ( x - 3)
y - 3 = -[tex]\frac{4}{5}[/tex] x + [tex]\frac{12}{5}[/tex]
y = -[tex]\frac{4}{5}[/tex] x + 3 + [tex]\frac{12}{5}[/tex]
y = -[tex]\frac{4}{5}[/tex] x + [tex]\frac{27}{5}[/tex]
5y = -4x + 27
