Perpendicular Line Equation
How to find the linear equation that is perpendicular to the given line: definition, formula, 1 example, and its solution.
Perpendicular Lines are the lines that form a right angle: 90 degrees.
The red symbol is the right angle symbol.
m1⋅m2 = -1
m1, m2: Slopes of the perpendicular lines
It says the line is perpendicular to y = 3x + 4.
Set the slope of the line you're looking for as m.
Then, by the formula,
3⋅m = -1.
Divide both sides by 3.
Then m = -1/3.
The slope, m, is -1/3.
And the line passes through (3, 1).
So the linear equation in point-slope form is
y = (-1/3)(x - 3) + 1.
Change the linear equation to slope-intercept form.
Then y = (-1/3)x + 2.
So y = (-1/3)x + 2 is the answer.
The purple slope line is the given line y = 3x + 4.
And the blue slope line is the answer y = (-1/3)x + 2.
y = (-1/3)x + 2 is perpendicular to y = 3x + 4.
And it passes through (3, 1).