Final answer:
The equation of the line that crosses the x-axis at four and is perpendicular to y = -2/3x + 4, in slope-intercept form, is y = (3/2)x - 6.
Step-by-step explanation:
The equation of the line that crosses the x-axis at four and is perpendicular to the line represented by y = -2/3x + 4 can be found by first determining the slope of the perpendicular line. Since the original line has a slope of -2/3, the slope of the perpendicular line will be the negative reciprocal, which is 3/2. The line that crosses the x-axis at four does so at the point (4,0), which will be a point on our new line.
Using the slope-point form of a line (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we get:
(y - 0) = (3/2)(x - 4)
Simplify this equation to get it into slope-intercept form:
y = (3/2)x - 6
Therefore, the equation of the line that crosses the x-axis at four and is perpendicular to the line y = -2/3x + 4 in slope-intercept form is y = (3/2)x - 6.