Write the equation a line in slope ¬intercept form with the given conditions: perpendicular to the line y = (⅔)x ¬ 1 and passes through the point (4, 7).

The slope-intercept form of the equation of a line is given as:

y = mx + c

where m is the slope of the line and c is the intercept.
In this question, we are given with the equation of a line which is perpendicular to our desired line and the coordinates of a point through which the desired line passes.
The equation of the line perpendicular to the desired line is:

y = (2/3)x - 1

This equation is already in the slope intercept form and thus, the slope of this line is 2/3.
The lines that are perpendicular to each other have opposite-reciprocal slopes, In other words, the product of the slopes of two perpendicular lines is -1.
Thus, m x (2/3) = -1
where m is the slope of our desired line.
Solving the above equation, we get: m = -3/2.
Thus, the equation of the desired line can be simplified as: y = (-3/2) x + c.
Now, this line passes through a point with coordinates of (4, 7). This means that (4, 7) is a solution of this line or when x = 4, then y = 7.
Substituting the values of x and y into the equation, we get:

7 = (-3/2) * 4 + c

solving this equation, we get: c = 13.
Thus, the equation of the line is y = (-3/2) x + 13.

Hope this helps.