To write the equation of a perpendicular line to the given equation, we first need to determine its slope.
Calculating the Slope of the Perpendicular Line
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 - 12.
y=-1/2x-4
By substituting this value into our negative reciprocal equation for m_1, we can solve for the slope of the perpendicular line, m_2.
With this, we can identify that any line perpendicular to the given equation will have a slope of 2.
Calculating the Point
Before we continue writing the equation for the perpendicular line, we will calculate the x-intercept of the given equation. To do this, we will substitute 0 for y and solve for x.
An x-intercept of - 8 means that the graph intercepts the x-axis at the point (- 8,0).
Writing the Equation of the Perpendicular Line
Using the slope m_2=2, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation.
y=2x+b
By substituting the given point ( - 8, 0) into this equation for x and y, we can solve for the y-intercept b of the perpendicular line.
