Question

Write an equation in slope-intercept form of the line that passes through (2,0) and is perpendicular to y=1/5 x-2.

Answer 1

Answer:

$y = -5x+10$

Step-by-step explanation:

Given

$(x_1,y_1) = (2,0)$

$y = \frac{1}{5}x - 2$

Required

Determine an equation that perpendicular to the equation

An equation has the form:

$y = mx + b$

Where

$m = slope$

By comparison:

$m = \frac{1}{5}$

Next, we determine the slope of the new line.

When two lines are perpendicular, the following relation exist:

$m_2= -\frac{1}{m_1}$

Substitute 1/5 for m1

$m_2= -\frac{1}{1/5}$

$m_2= -5$

The equation of the line is then calculated using:

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

Where:

$m_2= -5$ and $(x_1,y_1) = (2,0)$

This gives:

$y - 0 = -5(x - 2)$

$y = -5(x - 2)$

$y = -5x+10$