Final answer:
The equation in standard form of the line with slope -4/3 that passes through the point (4, 6) is 4x + 3y = 34. Finally, converting to standard form, we obtain 4x + 3y = 34.
Step-by-step explanation:
To find the equation of a line in standard form, we need the slope and a point on the line.
Given the slope m = -4/3 and the point (4, 6), we can use the point-slope form of a linear equation: y - y1 = m(x - x1).
Substituting the values, we get y - 6 = (-4/3)(x - 4).
Expanding and rearranging the equation, we get 3y - 18 = -4x + 16.
Finally, converting to standard form, we obtain 4x + 3y = 34.