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 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.
y=-3x -1
In the given equation, we can see that its slope is -3. 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 13.
Writing the Perpendicular Line's Equation
With the slope m_2=13, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation.
y=1/3x+b
By substituting the given point ( -3, 5) 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 perpendicular to y=-3x-1 and passes through the point (-3,5).
y=1/3x+6
