A line passes through (3,7) and (6,9). Which equation represents the line?
To find the equation representing the line passing through (3, 7) and (6, 9), we first need to find the slope of the line.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (3, 7) and (6, 9), we can substitute the values into the slope formula:
m = (9 - 7) / (6 - 3)
m = 2 / 3
So, the slope of the line is 2/3.
To find the equation of the line, we can use the point-slope form of a line, which is:
y - y1 = m(x - x1)
Substituting the values of the slope (m) and one of the points (x1, y1), we get:
y - 7 = (2/3)(x - 3)
Now, we can simplify the equation:
y - 7 = (2/3)x - 2
y = (2/3)x - 2 + 7
y = (2/3)x + 5
Therefore, the equation representing the line passing through (3, 7) and (6, 9) is y = (2/3)x + 5.