Answer:
We can use the point-slope form of the equation of a line to find the equation that passes through the points (3, 5) and (6, 7).
The point-slope form of a line is:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line and m is the slope of the line.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two points.
Plugging in the values we know, we get:
m = (7 - 5) / (6 - 3) = 2 / 3
So the slope of the line is 2/3.
Now we can use one of the given points and the slope to write the equation of the line in point-slope form. We'll use the first point, (3, 5).
y - 5 = (2/3)(x - 3)
This is the equation of the line in point-slope form.
If we want to write it in slope-intercept form (y = mx + b), we can simplify:
y - 5 = (2/3)x - 2
y = (2/3)x + 3
So the equation of the line that passes through the points (3, 5) and (6, 7) is y = (2/3)x + 3.