To write the equation of a perpendicular line to the given equation, we first need to determine its slope.
Perpendicular Line's Slope
Two lines are perpendicular when their slopes are opposite reciprocals. This means that the product of their slopes will be -1.
m_1*m_2=-1
For any equation written in slope-intercept form, y=mx+b, we can identify its slope as the value of m.
Looking at the given equation, we can see that its slope is - 3.
y=- 3x + 2
By substituting this value into our opposite reciprocal equation for m_1, we can solve for the slope of a perpendicular line, m_2.
Any perpendicular line to the given one will have a slope of 13.
Writing the Perpendicular Line's Equation
Using the slope m_2=13, we can write a general equation in slope-intercept form for all lines that are perpendicular to the given one.
y=1/3x+b
Since we are told the perpendicular line passes through the point (0,0), we will substitute 0 for both x and y in the above equation, and solve for the y-intercept b of the perpendicular line.
