Which of the following is an equation of the line A graphed in the xy-plane that passes through the point (-1,3.5) and is perpendicular to the line B whose equation is x+4.5=0 ? Choose 1 answer: (A) x=-1 (B) x=3.5 (C) y=3.5 (D) y=4.5

Question

Which of the following is an equation of the line  A graphed in the  xy-plane that passes through the point  (-1,3.5) and is perpendicular to the line  B whose equation is  x+4.5=0 ? Choose 1 answer: (A)  x=-1 (B)  x=3.5 (C)  y=3.5 (D)  y=4.5

Bytelearn · Accepted Answer

Understanding Line B: The question prompt is: ＂What is the equation of the line A in the xy-plane that passes through the point (-1,3.5) and is perpendicular to the line B whose equation is x+4.5=0?＂Perpendicularity and Horizontal Lines: First, we need to understand the equation of line B, which is given as x + 4.5 = 0. This is a vertical line because it has no y-term, and its slope is undefined. The line passes through all points where x = -4.5.Determining the Value of k: Since line A is perpendicular to line B, and line B is vertical, line A must be horizontal. A horizontal line has a slope of 0, which means its equation will be of the form y = k, where k is a constant.Equation of Line A: Line A passes through the point (-1, 3.5). Since line A is horizontal, the y-coordinate of every point on line A is the same. Therefore, the value of k must be 3.5.The equation of line A is y = 3.5. This matches one of the answer choices provided.

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