To write the equation of a line perpendicular to the given equation, we first need to determine its slope. After that, we will write a general equation and use the given point to determine the y-intercept.
Calculating the Slope of the Perpendicular Line
Two lines are perpendicular when their slopes are negative reciprocals. This means that the product of the slopes of perpendicular lines is -1.
m_1* m_2=-1
Note that the given equation is written in slope-intercept form.
y= 1/2x-9
In the above formula we can see that the slope is 12. By substituting this value for m_1 in our negative reciprocal equation, we can solve for the slope of the perpendicular line m_2.
Any perpendicular line to the given equation will have a slope of -2.
Writing the Equation of the Perpendicular Line
Let's write a partial equation in slope-intercept form for a line perpendicular to the given equation.
y= -2x+ b
By substituting the given point ( 7, 10) into this equation for x and y, respectively, we can solve for the y-intercept b of the perpendicular line.
