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What is an equation of a line that is perpendicular to the line whose equation is and passes through ?

Responses


y is equal to negative 2 thirds x minus 3


y is equal to 2 thirds x plus 1


y is equal to negative 2 thirds x minus 5

1 answer

To determine the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow these steps:

  1. Identify the slope of the given line: If the equation of the line is in the slope-intercept form \(y = mx + b\), where \(m\) is the slope.

  2. Calculate the slope of the perpendicular line: The slope of a perpendicular line is the negative reciprocal of the original line's slope. If the original slope is \(m\), the slope of the perpendicular line will be \(-\frac{1}{m}\).

  3. Use the point-slope form of the line equation: If you are given a point \((x_1, y_1)\) through which the perpendicular line passes, you can use the point-slope form of the equation: \[ y - y_1 = m_{perpendicular}(x - x_1) \] where \(m_{perpendicular}\) is the slope calculated in step 2.

Since you haven't provided the specific line or the point through which the perpendicular line passes, I can’t give you the exact equation. Please provide the equation of the original line and the coordinates of the point to continue. However, I can guide you through how to compute this if you share that information!