Mathematics
Grade9
Easy

Question

A line passes through the points (7, -1) and (2, 5). Where does the line intersect the y-axis?

  1. -8
  2. 37 over 5
  3. 7
  4. fraction numerator negative 37 over denominator 5 end fraction

hintHint:

To find the point where the line intersects with y axis we will first find the equation of the line using two point form equals left parenthesis y minus y subscript 1 right parenthesis 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 then rearrange it in the slope intercept form. With the equation we can find the y intercept.

The correct answer is: 37 over 5


    Line passes through the point (2,5) and (7,-1).
    So the equation of the lineequals left parenthesis y minus y subscript 1 right parenthesis 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
    rightwards double arrow left parenthesis y minus 5 right parenthesis equals fraction numerator negative 1 minus 5 over denominator 7 minus 2 end fraction left parenthesis x minus 2 right parenthesis
rightwards double arrow y minus 5 equals fraction numerator negative 6 over denominator 5 end fraction left parenthesis x minus 2 right parenthesis
rightwards double arrow y minus 5 equals fraction numerator negative 6 over denominator 5 end fraction x plus 12 over 5
rightwards double arrow y equals fraction numerator negative 6 over denominator 5 end fraction x plus 12 over 5 plus 5
rightwards double arrow y equals fraction numerator negative 6 over denominator 5 end fraction x plus 37 over 5
    So. the y intercept is 37 over 5.

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