Answer:
Using the point-slope form of the equation, the equation of the line passing through (-1,0) and perpendicular to the line is:
[tex]y=-3x-3[/tex]
Step-by-step explanation:
We know the slope-intercept of line equation is
[tex]y=mx+b[/tex]
where m is the slope, and b is the y-intercept
Given the line
[tex]y=\:\frac{1}{3}x-7[/tex]
Thus, the slope of the line is:
m=1/3
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be: -3
Therefore, using the point-slope form of the equation, the equation of the line passing through (-1,0) and perpendicular to the line is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-0=-3\left(x-\left(-1\right)\right)[/tex]
[tex]y=-3\left(x+1\right)[/tex]
[tex]y=-3x-3[/tex]
