What is an equation of a line that is perpendicular to the line whoseequation is 2y = 3x - 10 and passes through (6,1) ?

Answer: y = - 2x/3 + 5

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m represents the slope of the line.

c represents the y intercept.

The equation of the given line is

2y = 3x - 10

Dividing through by 2, it becomes

y = 3x/2 - 5

Comparing with the slope intercept form, slope = 3/2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line passing through (6, 1) is - 2/3

To determine the intercept, we would substitute m = - 2/3, x = 6 and y = 1 into y = mx + c. It becomes

1 = - 2/3 * 6 + c

1 = - 4 + c

c = 1 + 4 = 5

The equation becomes

y = - 2x/3 + 5