Maths-
General
Easy

Question

# In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?

Hint:

## The correct answer is: 3x +2y = 6

### Solution:- Option A)  3x +2y =6  is correct. The equation −2x + 3y = 6 can be rewritten in the slope-intercept form as follows: y = (2/3)x + 2. Comparing with the standard equation y = mx+ c So the slope of the graph of the given equation is 2/3 In the xy-plane, when two nonvertical lines are perpendicular, the product of their slopes is −1. So, if m is the slope of a line perpendicular to the line with equation           y = (2/3)x+ 2, then m × (2/3)= −1, which gives m = -3/2 Of the given choices, only the equation in choice A can be rewritten in the form y = -(-3/2) x +b, for some constant b. Therefore, the graph of the equation in choice A is perpendicular to the graph of the given equation. Options B, C, and D are incorrect because the graphs of the equations in these choices have slopes, respectively, of -3/4 ,-1/2 , and -1/3 but not -3/2. Therefore correct option is A)3x +2y =6

The slope-intercept form is one of the most common ways to represent a line's equation. For example, the slope of a straight line, slope-intercept, and y-intercept formula determine the equation of a line (where the line intersects the y-axis at the point of the y-coordinate). An equation must be satisfied by each point on a line. For example, the graph of the linear equation y = mx + c is a line with slope m and y-intercept m and c. This is known as the slope-intercept form of the linear equation, and the values of m and c are real numbers.
¶A line's slope, m, represents its steepness. Sometimes the slope of a line is referred to as the gradient. A line's y-intercept, b, represents the y-coordinate of the point where the line's graph intersects the y-axis.