Final answer:
To write the equation of a line parallel to AB, we need to determine the slope of AB and a point on the line. Using the points A (-3,0) and B (6,3), we calculate the slope of AB as 1/3. Then, we choose a point on the line and find the y-intercept. Using point A, the equation of the line parallel to AB is y = (1/3)x + 1.
Step-by-step explanation:
To find the equation of a line parallel to AB, we need to determine the slope of line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points A (-3,0) and B (6,3), we can calculate the slope as follows:
slope_AB = (3 - 0) / (6 - (-3)) = 3/9 = 1/3
Therefore, any line parallel to AB will have the same slope of 1/3. Now we can write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. Since the line is parallel to AB, we can choose any point on the line to determine the y-intercept. Let's choose point A (-3,0):
y = (1/3)x + b
0 = (1/3)(-3) + b
b = 1
Therefore, the equation of a line parallel to AB is y = (1/3)x + 1.