SOLUTION: What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x � 3 in slope-intercept form?

Question 636324: What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x � 3 in slope-intercept form?
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula:

where is the perpendicular slope

So plug in the given slope to find the perpendicular slope

When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second

Multiply the fractions.

So the perpendicular slope is

So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (0,2), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

where m is the slope and (,) is the given point

Plug in , , and

Distribute

Multiply

Add to both sides to isolate y

Make into equivalent fractions with equal denominators

Combine the fractions

Reduce any fractions

So the equation of the line that is perpendicular to and goes through (,) is

So here are the graphs of the equations and

graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Using the standard slope-intercept form for an equation of a line y = mx + b
where m is the slope and b the y-intercept.
line passing through (0, 2) and perpendicular to the line y = 4x � 3, m = 4
New Line: Note: negative reciprocal of 4
y = (-1/4)x + b
2 = (-1/4)�0 + b |Using ordered pair (x,y): (0,2) to solve for b
2 = b
y = (-1/4)x + 2

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