Final answer:
To find the equation of a line in point-slope form, we need the slope of the line and the coordinates of one point on the line. For the given points (6,6) and (7,3), the slope is -3. Plugging one of the points into the point-slope form equation gives us y - 6 = -3x + 18.
Step-by-step explanation:
To write the equation of a line in point-slope form, we need to know the slope of the line and the coordinates of one point on the line. The formula for point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Given the coordinates (6,6) and (7,3) of two points on the line, we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1).
Plugging in the values, we have: m = (3 - 6) / (7 - 6) = -3.
Next, we choose one of the points, let's say (6,6), and substitute the values into the point-slope form equation:
y - 6 = -3(x - 6).
Simplifying the equation gives us: y - 6 = -3x + 18.
This is the equation of the line through the given points in point-slope form.