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 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.
y= 4/3x+ 6
In the given equation we can see that its slope is 43. 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 - 34.
Writing the Equation of the Perpendicular Line
With the slope m_2= - 34, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation.
y= - 34x+ b
By substituting the given point ( -4, -1) into this equation for x and y, we can solve for the y-intercept b of the perpendicular line.
Now that we have the y-intercept, we can write the equation for the line that is both perpendicular to y= 43x+6 and passes through the point (-4,-1).
y= -3/4x -4
