Final answer:
The equation of the line perpendicular to y = -0.3x + 6 and passing through the point (3, -8) is y = 3.33x - 17.99.
Step-by-step explanation:
The given equation of the line is y = -0.3x + 6. To find a line perpendicular to this, we need to find the negative reciprocal of the slope. The slope of the given line is -0.3, so the slope of the perpendicular line will be 1/0.3 = 3.33 (rounded to two decimal places).
Using the point-slope form of a line, we can write the equation of the perpendicular line as y - y1 = m(x - x1), where (x1, y1) is the given point (3, -8) and m is the slope of the line. Substituting the values, we get y - (-8) = 3.33(x - 3).
Simplifying the equation, we have y + 8 = 3.33x - 9.99. Rearranging the terms, the equation of the line perpendicular to y = -0.3x + 6 and passing through the point (3, -8) is y = 3.33x - 17.99.