In the xy -plane, line s passes through the point 0 , 0 and is parallel to the line represented

Question

In the xy -plane, line s passes through the point 0 , 0 and is parallel to the line represented by the equation y = 18 x + 2 . If line s also passes through the point 4 , d , what is the value of d ?

Accepted Answer

Choice C is correct. A line in the xy -plane can be represented by an equation of the form y = m x + b , where m is the slope and b is the y -coordinate of the y -intercept of the line. It's given that line s passes through the point 0 , 0 . Therefore, the y -coordinate of the y -intercept of line s is 0 . It's also given that line s is parallel to the line represented by the equation y = 18 x + 2 . Since parallel lines have the same slope, it follows that the slope of line s is 18 . Therefore, line s can be represented by the equation y = m x + b , where m = 18 and b = 0 . Substituting 18 for m and 0 for b in y = m x + b yields the equation y = 18 x + 0 , or y = 18 x . If line s passes through the point 4 , d , then when x = 4 , y = d for the equation y = 18 x . Substituting 4 for x and d for y in this equation yields d = 18 4 , or d = 72 . Choice A is incorrect. This is the y -coordinate of the y -intercept of the line represented by the equation y = 18 x + 2 . Choice B is incorrect. This is the slope of the line represented by the equation y = 18 x + 2 . Choice D is incorrect. The line represented by the equation y = 18 x + 2 , not line s , passes through the point 4 , 74 .

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