Question
Show m = 2 for the straight line 8x - 4y = 12.
Hint:
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](data:image/png;base64,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)
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 convert this equation in the slope intercept form, which is
Where m is the slope of the line and c is the y-intercept.
We rewrite the equation 8x - 4y = 12, as below
Dividing the above equation by (-4) throughout, we get
Simplifying, we have
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 = and y-intercept =
, 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