Final answer:
The slope of line a is -1, the slope of line b is 1, and the equation for line b in point-slope form is y = x - 4.
Step-by-step explanation:
a. To find the slope of line a, we use the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates (5, -2) and (7, -4), we get: slope = (-4 - (-2)) / (7 - 5) = -2 / 2 = -1.
b. Since line b is perpendicular to line a, its slope will be the negative reciprocal of the slope of line a. So, the slope of line b is 1.
c. To find the equation of line b in point-slope form, we can use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the point (-2, -6) and slope 1, we get: y - (-6) = 1(x - (-2)). Simplifying, we have: y + 6 = x + 2. Rearranging the equation, the equation for line b in point-slope form is: y = x - 4.
Learn more about slope of lines