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Geometry Smart Math

[Smart Math] Geometry Problem 6

Here’s and example of a SMART MATH problem for GEOMETRY.

Geometry

Problem

Find the equation of a line with slope –4 and passing through the point (4, 5).

  1. x + y = 9
  2. x + 4y = 11
  3. 4x + y = 21
  4. 3x + 2y = 10
  5. 5x + y = 30

The Usual Method

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Using the point slope form of equation of a straight line, we get:

\left( y-5 \right)=-4\left( x-4 \right)

\therefore y-5=-4x+16

\therefore 4x+y=21

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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We already know the slope intercept form as y = mx + c.

The slope here is given as –4.

Thus, y = –4x + c or 4x + y = c

Thus, the coefficient of x should be 4.

Only option ‘3’ satisfies this condition and hence it is the answer.

(Ans: 3)

Estimated Time to arrive at the answer = 5 seconds.
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