Points (2, 0) and (0, 3) lie on line k. what is the slope of the line that is perpendicular to k? a. 3/2 b. - 3/2 c. 2/3 d. undefined

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

here x₁ = 2 and x₂ = 0 and y₁ = 0 and y₂ = 3

⇒ Slope of the line k is

We know that : If two lines are perpendicular, then the product of slopes of the two lines should be equal to -1

⇒ Slope of line k × Slope of line perpendicular to k = -1

⇒

⇒ Slope of line perpendicular to line =  

Option C is the Answer

C:  2/3

Step-by-step explanation:

Line k passes thru Points (2, 0) and (0, 3).  As we move from (2,0) to (0,3), x decreases by 2 to 0 and y increases by 3 to 3.  Thus, the slope of this line k is m = rise / run = -3 / 2.

Any line perpendicular to line k has a slope that is the negative reciprocal of -3/2.  In other words, such a line has the slope 2/3.  Answer C is correct.

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step-by-step explanation: