Maths-
General
Easy

Question

Show m = 2 for the straight line 8x - 4y = 12.

hintHint:

We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

The correct answer is: m = 2 for the straight line 8x - 4y = 12


    Step by step solution:
    The slope/ gradient of a line is denoted by m.
    The given equation of the line is

    8x - 4y = 12
    We convert this equation in the slope intercept form, which is

    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation 8x - 4y = 12, as below

    -4y = -8x - 12
    Dividing the above equation by (-4) throughout, we get

     fraction numerator negative 4 over denominator negative 4 end fraction y equals fraction numerator negative 8 over denominator negative 4 end fraction x minus fraction numerator 12 over denominator negative 4 end fraction
    Simplifying, we have

    y = 2x + 3
    Comparing with y = mx + c, we get that m = 2
    Thus, m = 2 for the straight line 8x - 4y = 12
     

    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative straight a over straight b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get m equals negative fraction numerator 8 over denominator negative 4 end fraction equals 2

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