A line passes through (3,7) and (6,9). Which equation represents the line?

Answer 1

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.