To write the equation of a line perpendicular to the given equation, we first need to determine its slope.
The Perpendicular Line's Slope
Two lines are perpendicular when their slopes are negative reciprocals. This means that the product of a given slope and the slope of a line perpendicular to it 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 - 9.
y=- 9x - 1
By substituting this value into our negative reciprocal equation for m_1, we can solve for the slope of a perpendicular line, m_2.
Any line perpendicular to the given equation will have a slope of 19.
Writing the Perpendicular Line's Equation
Using the slope m_2=19, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation.
y=1/9x+b
We are asked to write the equation of a line perpendicular to the given equation that passes through the given point (0, ). This point is the y-intercept of the perpendicular line. In this case, we do not need to perform any further calculations to find the value of b.
y=1/9x+ ⇔ y=1/9x
Finally, we can verify our answer by graphing both lines on the same coordinate plane. If they are perpendicular, they will intersect at a right angle.
We can see by looking at the graphs of the functions that they are indeed perpendicular.
