Find an equation of the line that passes through the point (2, 1) and is perpendicular to the line x + 2y=-2

2x - y = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 2y = - 2 ( subtract x from both sides )

2y = - x - 2 ( divide all terms by 2 )

y = - x - 1 ← in slope- intercept form

with slope m = -

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute (2, 1) into the partial equation

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = 2x - 3 ← equation in slope- intercept form

add 3 to both sides

y + 3 = 2x ( subtract y from both sides )

3 = 2x - y, thus

2x - y = 3 ← equation in standard form

]