Question

question
line u passes through the points (0, -4) and (0, 6). what is the equation for the
line which is perpendicular to u and passes through the point (-5, 2)?
answer
attempt 1 out of 2
x = -5
y = -5
x = 2
y = 2
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Explanation:

Step1: Find the slope of line \(u\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given two points \((x_1,y_1)=(0,-4)\) and \((x_2,y_2)=(0,6)\) on line \(u\), then \(m_u=\frac{6-(-4)}{0 - 0}\), which is undefined. So line \(u\) is a vertical line (\(x = 0\)).

Step2: Determine the slope of the perpendicular line

A line perpendicular to a vertical line is a horizontal line. The slope of a horizontal line \(m = 0\).

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

The point - slope form is \(y-y_1=m(x - x_1)\), where \(m = 0\) and \((x_1,y_1)=(-5,2)\). Substituting into the formula: \(y-2=0\times(x + 5)\).

Step4: Simplify the equation

Simplifying \(y-2=0\times(x + 5)\) gives \(y=2\).

Answer:

\(y = 2\)