Final answer:
To find the equation of line h perpendicular to line g, we need to find the negative reciprocal of the slope of line g and use the given point (3, -9). The equation of line h is y = -10/3x + 1.
Step-by-step explanation:
Line g can be written as y = 3/10 x - 8. To find a line perpendicular to line g, we need to find the negative reciprocal of the slope of line g. The slope of line g is 3/10, so the negative reciprocal is -10/3.
Since line h passes through the point (3, -9), we can use the point-slope form of a line to find the equation. The equation is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get y - (-9) = -10/3(x - 3).
Simplifying the equation gives us y + 9 = -10/3x + 10. We can further simplify it to get the final equation of line h as y = -10/3x + 1.