Answer:
Let's see what to do buddy..
Step-by-step explanation:
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STEP (1)
We have to first find the slope of the given line. To do that we must write the given line to slope-intercept form.
[tex]5x - 3y = 8[/tex]
Subtract the sides of the equation minus 5x :
[tex] - 3y = 8 - 5x \\ - 3y = - 5x + 8[/tex]
Divided the sides of the equation by -3 :
[tex] \frac{ - 3}{ - 3}y = \frac{ - 5x + 8}{ - 3} \\ \\ y = \frac{5}{3}x - \frac{8}{3} [/tex]
We know that the slope-intercept form of the linear functions is like this :
[tex]y = a \: x + b[/tex]
Where a is the slope and b is width of origin.
So the slope of the given line is 5/3.
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STEP (2)
The slopes of two lines perpendicular to each other are symmetrical and inverse to each other.
In other words, the product of the slopes of two lines perpendicular to each other is -1 .
So :
[tex] \frac{5}{3} \times (t) = - 1 \\ [/tex]
Divided the sides of the equation by 5/3 :
[tex] \frac{ \frac{5}{3} }{ \frac{5}{3} } \times t = \frac{ - 1}{ \frac{5}{3} } \\ \\ t = - \frac{3}{5} [/tex]
((t)) is the slope of the line which we want to find.
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STEP (3)
We have this equation to find the slope-intercept form of the linear functions :
[tex]y - y(given \: point) = (slope) \times ( \: x - x(g \: p) \: ) \\ [/tex]
Now Just need to put the slope and the given point in the equation:
given point = ( -5 , 2 )
slope = -3/5
[tex]y - 2 = - \frac{3}{5}(x - ( - 5)) \\ y - 2 = - \frac{3}{5}(x + 5) \\ y - 2 = - \frac{3}{5}x - 3 \\ [/tex]
Subtract the sides of the equation plus 2 :
[tex]y = - \frac{3}{5}x - 1 \\ [/tex]
And we're done.
Thanks for watching buddy good luck.
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