Which of the following is/are true of the lines 2x

Question

Which of the following is/are true of the lines 2x - 5y = -15 and 5x + 2y = 6? (I) They are parallel.
(II) They are perpendicular.
(III) They cross the x-axis at the same point.
(IV) They cross the y-axis at the same point.

Quizplus · Accepted Answer

To determine if two lines are perpendicular, we need to check if the product of their slopes is -1. The slope of the first line is 2/5 and the slope of the second line is -5/2. Their product is (-5/2) * (2/5) = -1, so the lines are perpendicular. 
To find where the lines cross the x-axis, we set y = 0 and solve for x. For the first line, we get 2x = 15, so x = 15/2. For the second line, we get 5x = 6, so x = 6/5. Since these values are not equal, the lines do not cross the x-axis at the same point. 
To find where the lines cross the y-axis, we set x = 0 and solve for y. For the first line, we get -5y = -15, so y = 3. For the second line, we get 2y = 6, so y = 3. Since these values are equal, the lines do cross the y-axis at the same point. Therefore, our final answer is D, II and IV.