I presume that since you labeled this as a Calculus problem that you mean x * 4y = 12?
x * 4y = 12 --->
4y = 12 / x --->
y = 3 / x --->
y = 3 * x^(-1)
You will notice that this function is not a line, but a curve. The slope will be different at different points on the line. Thus, we can't find the slope of the entire function, but we CAN find a function which gives us the slope of a tangent line at any point on the function. We do this by taking the derivative.
For f(x) = a * x^(n)
f'(x) = a * n * x^(n-1)
Using a = 3 and n = -1, we have:
y = f(x) = 3 * x^(-1)
dy/dx = f'(x) = 3 * -1 * x^(-1 - 1) = -3 * x^(-2)
So your answer will be:
dy/dx = -3 * x^(-2)
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3x + 4y = 12 Subtract 3x from each side 4y = 12 - 3x Divide by 4 on each side y = 3 - .75x The slope is what is multiplied by "x" or -.75
x -4y = 4 -4y = -x +4 y = 1/4x -1 So the slope is 1/4 and the y intercept is -1.
The equation must be rearranged into slope-intercept form. 4y - 8x + 12 = 0 4y +12 = 8x 4y = 8x -12 y = 2x - 6 Now we have proper slope-intercept form: y = 2x - 6 (y = mx + b) The slope is the coefficient in front of the x variable and denoted by the letter m. Therefore... m = 2
Slope-intercept form is y = mx + b where m = slope and b = y intercept You need to get equation in slope-intercept form: 3x + 4y = 12 4y = 12 - 3x y = 3 - 3/4 x y = -3/4 x + 3 That means m = slope = -3/4 Parallel lines have the same slope, so the other line also has a slope of -3/4
3x-4x=12 that means -x equals 12 so x equals -12