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nordsb [41]
3 years ago
15

Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0

Answer:  2x+5y+10=0

Step-by-step explanation:

The equation of the given line : 5x - 2y = -6 which can be written as 2y=5x+6 or  y=\dfrac{5}{2}x+3 . (i)

Linear equation : y=mx+c, where m= slope and c = intercept.

Comparing this to (i), we get m=\dfrac{5}{2}, c=3

Let m_1 be the slope of the line perpendicular to the line 5x - 2y = -6 and passes through the point  (5,-4).

Since, the product of slopes of two perpendicular lines is -1.

So,

\dfrac{5}{2}\times m_1=-1\\\\\Rightarrow\ m_1=-\dfrac{2}{5}

Equation of line passes through (a,b) and have slope n is given by :-

(y-b)=n(x-a)

So, Equation of line passes through (5,-4) and have slope  \dfrac{2}{5} would be

(y-(-4))=\dfrac{-2}{5}(x-5)\\\\\Rightarrow\ 5(y+4)=-2(x-5)\\\\\Rightarrow\ 5y+20=-2x+10\\\\\Rightarrow\ 2x+5y+10=0

Required equation : 2x+5y+10=0

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