To find the equation of the line passing through (4, 7) and (1, 4) in slope-intercept form (y = mx + b), we need to first find the slope (m) of the line using the two points. The slope formula is:
m = (y2 - y1)/(x2 - x1)
Plugging in the coordinates of the two points, we get:
m = (4 - 7)/(1 - 4) = -3/-3 = 1
So the slope of the line is 1.
Now we can use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
We can choose either of the two points to plug in for (x1, y1). Let's use (4, 7):
y - 7 = 1(x - 4)
Simplifying this equation, we get:
y - 7 = x - 4
y = x + 3
Therefore, the equation of the line passing through (4, 7) and (1, 4) in slope-intercept form is y = x + 3.