Question

What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)

Answer 1

First, put the equation of the line given into slope-intercept form by solving for y. You get y = 2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point giveninto the equation y = 1/2x + b and solving for b, we get b = 6.

Answer 2

Answer:

$y = \displaystyle\frac{-1}{m}(x-5) + 3$

Step-by-step explanation:

The equation of the line is not given.

Let m be the slope of the given line.

Using this information we can solve the question in the following manner:

We are given the following in the question:

The line passes through the point (5, 3) and is perpendicular to line with slope m.

When lines are perpendicular, then the product of their slopes is -1.

$m_1\times m_2 = -1$

Slope =

$\displaystyle\frac{-1}{m}$

The point slope form of line can be written as:

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

Putting the values, we get:

$(y-3) = \displaystyle\frac{-1}{m}(x-5)\\\\y = \displaystyle\frac{-1}{m}(x-5) + 3\\\\m(y-3) = -1(x-5)$

The above equation is the required equation of the line.