Maths-
General
Easy

Question

The graph of a line in the x y-plane passes through the point (1, 4) and crosses the x-axis at the point (2, 0) . The line crosses the y-axis at the point (0, b) . What is the value of b ?

The correct answer is: b = 8


    HINT – Form equation of a straight line using two point form or point slope form
    SOLUTION -  It is given that the line pass through two points viz.
    (1 , 4) and (2 , 0)
    Slope of the line = fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction where (x, y1) and (x2 , y2) are two points through which line is passing.
    So, slope of the line fraction numerator 0 minus 4 over denominator 2 minus 1 end fraction equals fraction numerator negative 4 over denominator 1 end fraction equals negative 4
    We know that equation of a line is given by (y – y1) = m (x – x1) where m is the slope of the line. This is called point slope method.
    Equation of the line is (y – 0 ) = - 4 (x – 2)
    rightwards double arrowy = - 4x + 8
    rightwards double arrow4x + y = 8             ---- (1)
    Now, given point is (0 , b). Substituting in equation (1)
    We get, 4(0) + b = 8
    rightwards double arrowb = 8
    Hence, answer is b = 8

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