Answer: y = (3/2)x - 7
Step-by-step explanation:To find the equation of a line perpendicular to another line, we need to know that the slopes of two perpendicular lines are negative reciprocals of each other. Therefore, the slope of the line we're looking for will be the negative reciprocal of -2/3, which is 3/2.
Now we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
We know that the line we're looking for goes through the point (6,2), so x1 = 6 and y1 = 2. We also know that the slope is 3/2. Substituting these values into the point-slope form, we get:
y - 2 = (3/2)(x - 6)
Simplifying and putting the equation into slope-intercept form, we get:
y = (3/2)x - 7
So the equation of the line perpendicular to y = -2/3x -1 that goes through the point (6,2) is y = (3/2)x - 7.