Official Guide Explanation:
Problem Solving #102




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Solution and Metadata

Question: 102
Page: 74
Difficulty: 5 (Moderate)
Category 1: Geometry > Coordinate Geometry > Slope

Explanation: The equation of a line is y = mx + b, and we're given m = 2. We know the line goes through the origin, (0,0), so we can plug in those values for x and y to find the value of b:

0 = 2(0) + b

b = 0

So the equation of the line is y = 2x.

Given the equation, we can solve for the values of x and y in the two points. The point (3,y) is:

y = 2(3) = 6, so y = 6

The point (x,4) is:

4 = 2x, so x = 2

x + y = 2 + 6 = 8, choice (C).

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