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Blababa [14]
3 years ago
12

What is an equation of the line that passes through the point (-4,3) and is

Mathematics
1 answer:
Tom [10]3 years ago
3 0

Answer:

5x + 4y = - 8

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 )

Given

4x - 5y = 20 ( subtract 4x from both sides )

- 5y = - 4x + 20 ( divide all terms by - 5 )

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

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

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

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

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

To find c substitute (- 4, 3) into the partial equation

3 = 5 + c ⇒ c = 3 - 5 = - 2

y = - \frac{5}{4} x - 2 ← in slope- intercept form

Multiply through by 4

4y = - 5x - 8 ( add 5x to both sides )

5x + 4y = - 8 ← equation in standard form

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