Final answer:
The equation in slope-intercept form of the line perpendicular to y=-2/3x+4 and crossing the x-axis at 4 is y = 3/2x.
Step-by-step explanation:
To find the equation of the line that crosses the x-axis at 4 and is perpendicular to the line represented by y = -2/3x + 4, we need to determine the slope of the perpendicular line.
The slope of the given line is -2/3. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 3/2.
Since the line crosses the x-axis at 4, the y-intercept is 0. Therefore, the equation in slope-intercept form of the line that satisfies the given conditions is y = 3/2x.