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4 years ago

Write the equation of the line passing through (-3, 4) and normal to -2x + 7y = -3. (Note: normal means perpendicular)

Mathematics

1 answer:

MArishka [77]4 years ago

8 0

Answer:

The answer to your question is y = -7/2x -13/2

Step-by-step explanation:

Point = (-3, 4)

Line -2x + 7y = -3

Process

1.- Solve equation for y to find the slope of the perpendicular line

7y = 2x - 3

y = 2/7 x - 3/7

slope = 2/7

Slope of the perpendicular line = -7/2

2.- Find the equation of the new line

y - y1 = m(x - x1)

y - 4 = -7/2(x + 3)

y - 4 = -7/2x - 21/2

y = -7/2x - 21/2 + 4

y = -7/2x -21/2 + 8/2

3.- Result

y = -7/2x -13/2

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$x-2y=-16\\Adding\ 2y\ on\ both\ sides\\x=2y-16\\Adding\ 16\ on\ both\ sides\\x+16=2y-16+16\\x+16=2y\\2y=x+16\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{x+16}{2}\\y=\frac{x}{2}+\frac{16}{2}\\y=\frac{1}{2}x+8\\$