108k views
1 vote
Which equation describes a line passing through (4,-1) and perpendicular to y=2x-4? y=-(1)/(2)x+3

User Memememe
by
7.4k points

1 Answer

2 votes

Final answer:

The correct equation of the line perpendicular to y = 2x - 4 and passing through the point (4, -1) is y = (-1/2)x + 1, which has a negative reciprocal slope of -1/2, representative of perpendicular lines.

Step-by-step explanation:

The student is asking for an equation of a line that is perpendicular to a given line and passes through a specific point. The given line's equation is y = 2x - 4, which means the slope of this line is 2. For a line to be perpendicular to this, it must have a slope that is the negative reciprocal of 2, which is -1/2. Using the point-slope form, y - y1 = m(x - x1), with m as the slope and (x1, y1) as the given point (4, -1), we can find the equation of the perpendicular line.

To find the new equation, plug in the point and slope into the point-slope form to get y - (-1) = (-1/2)(x - 4), which simplifies to y + 1 = (-1/2)x + 2. Subtracting 1 from both sides gives us the final equation y = (-1/2)x + 1. Therefore, the correct equation describing the line perpendicular to y = 2x - 4 and passing through (4, -1) is y = (-1/2)x + 1, not y = -(1/2)x + 3 as mentioned in the student's question.

User Epichorns
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories