Maths-
General
Easy

Question

In the xy-plane, the point (2, 6) lies on the graph of y equals k over x   where k is a constant. Which of the following points must also lie on the graph?

  1. left parenthesis 1 comma 3 right parenthesis
  2. left parenthesis 1.4 right parenthesis
  3. left parenthesis 3 comma 3 right parenthesis
  4. left parenthesis 3 comma 4 right parenthesis

hintHint:

Hint:
Here, we are given a point on the xy plane and an equation which that point satisfies. This should help us to find the unknown constant k. By using this value of k, we get an equation that is satisfied by the point (2, 6). Next, we check which of the points given in the options satisfy this equation.

The correct answer is: left parenthesis 3 comma 4 right parenthesis


    Given, the point (2, 6) satisfies the equation  y equals k over x
    So, we get
    6 equals k over 2
    k = 12
    Thus, the equation becomes y equals 12 over x
    Next, we check which of the points in the options satisfy the equations y equals 12 over x
    A) (1 , 3)
    We can see that 3 not equal to 12 over 1  , that is 3 not equal to 12
    So, (1, 3) doesn’t satisfy the equation y equals 12 over x
    B) (1, 4)
    Clearly ,4 not equal to 12 over 1, that is,4 not equal to 12
    So, (1, 4) does not satisfy the equation y equals 12 over x
    C) (3, 3)
    Here , 3 not equal to 12 over 3  , that is ,3 not equal to 4
    Hence, (3, 3) also doesn’t satisfy the equation y equals 12 over x
    D) (3, 4)
    Clearly, 4 equals 12 over 3  , so we can say that the point (3, 4) satisfies the equation y equals 12 over x
    The correct option is D) (3, 4).



    .


     

    Note:
    Whenever there is an unknown constant in the given equation, we must always try to find the value of that constant first with the help of the given conditions. Another way to solve this question is; observe that the equation can be written as x y = k , that is, the product of the x co-ordinate and y co-ordinate always remains a constant. As the point (2, 6) satisfies it, we get that constant to be 12. So we check for which of the points in the options, the product of x co-ordinate and y co-ordinate is 12.

    Related Questions to study

    General
    Maths-

    Find the value of 'x' in the following expressions:(a) 12x – 9 = 5

    Find the value of 'x' in the following expressions:(a) 12x – 9 = 5

    Maths-General
    General
    Maths-

    Solve the following equations. (b) 4m + 11 = 55

    Solve the following equations. (b) 4m + 11 = 55

    Maths-General
    General
    Maths-

    y=x2 - a
    In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

    y=x2 - a
    In the equation above, a is a positive constant and the graph of the equation in the xy‑plane is a parabola. Which of the following is an equivalent form of the equation?

    Maths-General
    parallel
    General
    Maths-

    fraction numerator 2 x plus 6 over denominator left parenthesis x plus 2 right parenthesis squared end fraction minus fraction numerator 2 over denominator x plus 2 end fraction
    The expression above is equivalent to fraction numerator a over denominator left parenthesis x plus 2 right parenthesis squared end fraction, where a is a positive constant and
    x ≠ −2.  What is the value of a ?

    fraction numerator 2 x plus 6 over denominator left parenthesis x plus 2 right parenthesis squared end fraction minus fraction numerator 2 over denominator x plus 2 end fraction
    The expression above is equivalent to fraction numerator a over denominator left parenthesis x plus 2 right parenthesis squared end fraction, where a is a positive constant and
    x ≠ −2.  What is the value of a ?

    Maths-General
    General
    Maths-

    x2 + 20x + y2 + 16y = -20
    The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

    x2 + 20x + y2 + 16y = -20
    The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?

    Maths-General
    General
    Maths-


    The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?


    The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?

    Maths-General
    parallel
    General
    Maths-

    The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

    The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

    Maths-General
    General
    Maths-

    If a2 + b2 = z and ab = y, which of the following is equivalent to 4z + 8y ?

    If a2 + b2 = z and ab = y, which of the following is equivalent to 4z + 8y ?

    Maths-General
    General
    Maths-

    Intersecting lines r, s and t are shown below .

    Intersecting lines r, s and t are shown below .

    Maths-General
    parallel
    General
    Maths-

    The surface area of a cube is 6(a/4)2,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

    The surface area of a cube is 6(a/4)2,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

    Maths-General
    General
    Maths-

    table attributes columnspacing 1em end attributes row cell y equals x squared end cell row cell 2 y plus 6 equals 2 left parenthesis x plus 3 right parenthesis end cell end table
    If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

    table attributes columnspacing 1em end attributes row cell y equals x squared end cell row cell 2 y plus 6 equals 2 left parenthesis x plus 3 right parenthesis end cell end table
    If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

    Maths-General
    General
    Maths-


    In triangle ABC above, side AC is extended to
    point D. What is the value of y-x?

    Note:
    It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.


    In triangle ABC above, side AC is extended to
    point D. What is the value of y-x?

    Maths-General

    Note:
    It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

    parallel
    General
    Maths-

    A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

    A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, p people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of p ?

    Maths-General
    General
    Maths-

    In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T)  = 0.6T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

    In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, in degrees Celsius, and is given by S(T)  = 0.6T + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

    Maths-General
    General
    Maths-

    Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

    Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.