Final answer:
The equation of line h, which is perpendicular to line g (y + 3 = -½(x - 8)) and passes through the point (-1, -6), is y = 2x - 8.
Step-by-step explanation:
The equation of line g is given as y + 3 = -½(x - 8). This equation can be put in slope-intercept form to find the slope of line g.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
The given line has a slope of -½, which means for every 2 units increase in the x-direction, there is a 1 unit decrease in the y-direction.
To find a line perpendicular to line g, we'll need a slope that is the negative reciprocal of -½, which is 2.
Therefore, the slope of line h would be 2.
Since line h passes through the point (-1, -6), we can use the point-slope form y - y1 = m(x - x1) to find the equation of line h.
Plugging in the point (-1, -6) and the slope 2, the equation of line h is y + 6 = 2(x + 1).
Simplifying, we get the equation y = 2x - 8 for line h.