The equation of line is:
[tex]y = - \frac{1}{3}x-5[/tex]
Further explanation:
Given equation of line is:
y = 3x+5
The standard form of point-slope form is:
y = mx+b
Comparing the given equation with the standard form is:
m = 3
We know that product of slopes of two perpendicular lines is -1
Let m2 be the slope of line perpendicular to y = 3x+5
Then
[tex]3 * m_2 = -1\\m_2 = -\frac{1}{3}[/tex]
Putting the value of slope in standard form
[tex]y = -\frac{1}{3}x + b[/tex]
To find the value of b, putting (-3,-4) in equation
[tex]-4 = -\frac{1}{3}(-3) + b\\-4 = 1 + b\\b = -4-1\\b = -5[/tex]
Putting the values of slope and b in equation
[tex]y = - \frac{1}{3}x-5[/tex]
Keywords: Slope, Point-intercept form
Learn more about perpendicular lines at:
#LearnwithBrainly
