Mathematics
Grade9
Easy

Question

A line passes through the points (11, -3) and (5, 6). Where does the line intersect the x-axis?

  1. 8
  2. 5
  3. 7
  4. 9

hintHint:

To find the point of intersection of line with the x axis when the two points of the line are given we first need to find the equation of the line then we know that when the line will intersect the x axis y coordinate will be 0 at that point. So in the equation we will put 0 in the place of y and find the value of x which is the required point.

The correct answer is: 9


    Given, A line passes through the points (11, -3) and (5, 6).
    So, equation =y minus y subscript 1 equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction left parenthesis x minus x subscript 1 right parenthesis
    y minus left parenthesis negative 3 right parenthesis equals fraction numerator 6 minus left parenthesis negative 3 right parenthesis over denominator 5 minus 11 end fraction left parenthesis x minus 11 right parenthesis
y plus 3 equals fraction numerator 6 plus 3 over denominator negative 6 end fraction left parenthesis x minus 11 right parenthesis
y plus 3 equals fraction numerator 9 over denominator negative 6 end fraction left parenthesis x minus 11 right parenthesis
y plus 3 equals fraction numerator 3 over denominator negative 2 end fraction left parenthesis x minus 11 right parenthesis
minus 2 left parenthesis y plus 3 right parenthesis equals 3 left parenthesis x minus 11 right parenthesis
minus 2 y minus 6 equals 3 x minus 33
minus 2 y equals 3 x minus 33 plus 6
2 y equals negative 3 x plus 27
    We have to find x intercept So, y will be 0 at this point.
    2y=-3x+27
    0=-3x+27
    3x=27
    x=9
    so x intercept is 9.

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