Let's denote the coordinates of point 1 as (x1, y1) and those of point 2 as (x2, y2) respectively.
For point 1, we have (x1, y1) = (0,7) and for point 2, we have (x2, y2) = (4,4).
The linear equation of a line going through two points is given by the formula: y = mx + b, where 'm' is the slope of the line and 'b' is the y-intercept.
Step 1: Calculate the slope ('m') of the line using the formula: m = (y2 - y1) / (x2 - x1).
By substituting the given points into the formula, we get m = (4 - 7) / (4 - 0) = - 3 / 4 = -0.75.
Step 2: Find the y-intercept ('b') of the line. This is the y-coordinate of the point where the line crosses the y-axis. Since point 1 (0,7) lies on the y-axis (where x=0), the y-coordinate of this point gives the y-intercept. Therefore, b = y1 = 7.
So, the equation of the line that passes through the points (0,7) and (4,4) in slope-intercept form (y = mx + b) is y = -0.75x + 7.