Maths-
General
Easy

Question

negative 2 x plus 3 y equals 6
In the xy-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?

  1. 3x +2y = 6 
  2. 3x +4y = 6 
  3. 2x +4y = 6 
  4. 2x +6y = 3

hintHint:

Hint:- The slope-intercept form of a straight line is used to find the equation of a line.
For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis.
Using the slope-intercept formula, the equation of the line is:
y = mx + b
where, m = the slope of the line
  • b = y-intercept of the line
  • (x, y) represent every point on the line
    x and y have to be kept as the variables while applying the above formula.

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.

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