Perpendicular Line: y = 3x - 10
Explanation:
[tex]\sf {Given:} \ y = -\dfrac{1}{3} x-4[/tex]
Comparing it with slope intercept formula: [tex]\bf y = mx + b[/tex]
- where m is the slope, b is y intercept
Identify the slope for this particular function:
[tex]\star \ \ \sf slope = -\dfrac{1}{3}[/tex]
Now given that the line passes perpendicularly, then the slope shall be negatively inverse of the parallel slope.
[tex]\implies \sf \ perpendicular \ slope : \ -(\dfrac{1}{m} ) \ = \ -(\dfrac{1}{-1/3} ) \ = \ 3[/tex]
Now, find the equation:
[tex]y -y_1 = m(x - x_1) \ \ \ \ \textsc where \ (x_1, y_1 ) \ are \ points[/tex] given points : (6, 8)
equation:
[tex]\rightarrow \sf y - 8 = 3(x-6)[/tex]
[tex]\rightarrow \sf y = 3x-18+8[/tex]
[tex]\rightarrow \sf y = 3x-10[/tex]
