Write an equation of the line that passes through the point (4,0) and is perpendicular to y=-2x+1

Question

How do I find an equation based on that information 

Answer 1

You can express your answer in slope-intercept form: y = mx + b.  Where m is the slope and b is the y-intercept.

 

• The slope of the given equation y = -2x + 1 has a slope of m₁ = -2.
• The slope of any line perpendicular to it is m₂ = -1(-1/2) = 1/2. (Take the reciprocal of -2 and multiply by -1.)
• Thus find the equation of the line that is perpendicular and passes through the point (4,0).
• y = mx + b
• y = 1/2 x + b. Substitute coordinates of point (4,0) to find the y-intercept.
• 0 = 1/2(4) + b
• 0 = 2 + b
• -2 = b.            
• y = 1/2 x -2. Answer.

Answer 2

If perpendicular, its slope is the negative reciprocal of the slope of the given line.

 

m = -1/-2 = 1/2

 

In point-slope form,

 

y - y₁ = m(x - x₁)

 

y - 0 = (1/2)(x - 4)

 

y = (1/2)(x - 4)