To find the equation of the line that passes through the points (3, 7) and (6, 9), we can use the slope-intercept form of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to calculate the slope (m) using the formula:
m = (y2 – y1) / (x2 – x1)
Substituting in our points (x1, y1) = (3, 7) and (x2, y2) = (6, 9), we get:
m = (9 – 7) / (6 – 3) = 2 / 3
Now that we have the slope, we can use one of the points to find the y-intercept (b). Let’s use the point (3, 7):
7 = (2/3)(3) + b
Simplifying this, we find:
7 = 2 + b
b = 7 – 2
b = 5
Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the line:
y = (2/3)x + 5
This equation represents the line that passes through the points (3, 7) and (6, 9).