Question

Line p is represented by the equation 2x-y=-5. If line r passes through the point (6,4) and is perpendicular to line p, what is the equation of line r?

Answer 1

Answer:

$y = -\frac{1}{2}x + 7$

Step-by-step explanation:

Given

$2x - y = 5$

$Point = (6,4)$

Required

Determine the equation of perpendicular line, r

First we need to determine the slope of the given equation

$2x - y = 5$

Make y the subject:

$y = 2x - 5$

The general form of an equation is:

$y = mx + b$

Where:

$m = slope$

By comparison;

$m = 2$

Since both lines are perpendicular:

We have:

$m_1 = -1/m$ to calculate the slope of the perpendicular line

$m_1 = -\frac{1}{2}$

Equation of the line can be solved using:

$y - y_1 = m(x - x_1)$

Where

$(x_1,y_1) = (6,4)$

$m = m_1 = -\frac{1}{2}$

So: the equation becomes

$y - 4 = -\frac{1}{2}(x - 6)$

$y - 4 = -\frac{1}{2}x + 3$

Solve for y

$y = -\frac{1}{2}x + 3 + 4$

$y = -\frac{1}{2}x + 7$

Hence:

The required equation is

$y = -\frac{1}{2}x + 7$