Maths-
General
Easy

Question

In the x - y plane, the graph of line ell  has slope 3 . Line k  is parallel to line  ell and contains the point  ( 3, 10 ). Which of the following is an equation of line k ?

  1. y equals negative 1 third x plus 11
  2. y equals 1 third x plus 9
  3. y equals 3 x plus 7
  4. y equals 3 x plus 1

hintHint:

Hint:
We know that the slopes of parallel lines are equal in a xy-plane. So, we get slope of  k and a point on line k . We use the point slope form of a line to find the equation of k . The point slope form of a line is y - a = m( x - b ) , where m is slope and (a, b) is a point on the line.

The correct answer is: y equals 3 x plus 1


    Given,
    Slope of line  l = 3
    As, line  is parallel to l , their slopes are equal.
    So, slope of line  k (m) = 3
    Also,  passes through the point (3, 10)
    The equation of a line in point-slope form is given by
    y minus b equals m left parenthesis x minus a right parenthesis
    where, m  is the slope of the line and
    ( a, b ) is any point lying on the line.
    Using the above formula, the equation of line  is given by
    y minus 10 equals 3 left parenthesis x minus 3 right parenthesis
    Simplifying the above equation, we have
    y minus 10 equals 3 x minus 9
    Adding 10 both sides, we get
    y equals 3 x minus 9 plus 10
    Finally, we have
    y equals 3 x plus 1
    Hence, the equation of line  k is y = 3x + 1
    Thus, the correct option is D)

    Note:
    The general equation of a line is  Ax + By = c. This form is modified to give us many other forms of equation of a line which involve the use of slope, x intercept, y intercept, etc. The student needs to be familiar with all these forms of equation of a line.

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