Final answer:
The equation in point-slope form for the line passing through the points (3,5) and (-6,-4) is y - 5 = x - 3
Step-by-step explanation:
The equation in point-slope form for a line that passes through the given set of points (3,5) and (-6,-4) can be determined using the formula:
y - y1 = m(x - x1)
where (x1, y1) represents one of the points and m represents the slope of the line. First, we need to calculate the slope:
m = (y2 - y1) / (x2 - x1)
Using the given points (-6,-4) and (3,5), we can calculate the slope:
m = (-4 - 5) / (-6 - 3) = -9 / -9 = 1
Now we can choose one of the points, let's use (3,5), and substitute it into the point-slope formula:
y - 5 = 1(x - 3)
Therefore, the equation in point-slope form for the line that passes through the given points is:
y - 5 = x - 3