Which equation represents the line that passes through (6, 7) and (3, 6)?

To find the equation of the line that passes through the points (6, 7) and (3, 6), we can start by calculating the slope of the line using the slope formula:

Slope (m) = (y2 – y1) / (x2 – x1)

Here, we can assign (x1, y1) = (6, 7) and (x2, y2) = (3, 6). Plugging in these values:

m = (6 – 7) / (3 – 6) = (-1) / (-3) = 1/3

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

y – y1 = m(x – x1)

We can use one of the points. Let’s use (6, 7):

y – 7 = (1/3)(x – 6)

Next, we will simplify this equation:

y – 7 = (1/3)x – 2

Adding 7 to both sides:

y = (1/3)x + 5

This is the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Thus, the equation that represents the line passing through the points (6, 7) and (3, 6) is:

y = (1/3)x + 5