Answer:
The equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
Given the line
y = 3x - 2
comparing with the slope-intercept form of the line equation
The slope of the line y = 3x - 2 is: m = 3
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 3
Thus, the slope of the the new perpendicular line = – 1/m = -1/3 = -1/3
The point-slope form of the line equation is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
In our case:
now substituting the perpendicular slope m = -1/3 and (-9, 0) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-0=-\frac{1}{3}\left(x-\left(-9\right)\right)[/tex]
[tex]y=-\frac{1}{3}\left(x-\left(-9\right)\right)[/tex]
[tex]y=-\frac{1}{3}\left(x+9\right)[/tex]
[tex]\:\:y\:=-\frac{1}{3}x-3[/tex]
Therefore, the equation perpendicular to y = 3x - 2 and passing through (-9, 0) in the slope-intercept form will be:
