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Gre4nikov [31]
3 years ago
13

the straight line L has the equation 4y=5x+3. Point A has the coordinates (3,-2) Find the equation of the line straight line tha

t is perpendicular to L and passes through A. Write your answer in the form y-mx+c where m and c are decimals or fractions {3 marks}
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
4 0

Answer:

y = - \frac{4}{5} x + \frac{2}{5}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 4y = 5x + 3 into this form by dividing the 3 terms by 4

y = \frac{5}{4} x + \frac{3}{4} ← in slope- intercept form

with slope m = \frac{5}{4}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{5}{4} } = - \frac{4}{5} , thus

y = - \frac{4}{5} x + c ← is the partial equation

To find c substitute (3, - 2) into the partial equation

- 2 = - \frac{12}{5} + c ⇒ c = - 2 + \frac{12}{5} = \frac{2}{5}

y = - \frac{4}{5} x + \frac{2}{5} ← equation of perpendicular line

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\bf \boxed{5i+12j}\implies 
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