Express the following equation
6x-8y=8(x-9)+12 in:
1. Slope intercept form
2. Standard form
6x-8y=8(x-9)+12
6 x - 8 y = 8 x - 72 + 12
- 2 x - 8 y = - 60
x + 4 y = 30
y = -(1/4) x + 15/2
To express the equation 6x-8y=8(x-9)+12 in different forms, let's start by simplifying the right side of the equation.
1. Slope-intercept form (y = mx + b):
To express the equation in slope-intercept form, we need to rearrange it to isolate y.
6x - 8y = 8(x - 9) + 12
6x - 8y = 8x - 72 + 12 (distribute 8 to (x - 9))
6x - 8y = 8x - 60
Next, let's isolate the y-term by moving the x terms to the right side:
6x - 8y - 8x = -60
-2x - 8y = -60
Finally, divide the entire equation by -8 to get y:
(-2x - 8y) / -8 = -60 / -8
2x + y = 7
So, in slope-intercept form, the equation is y = -2x + 7.
2. Standard form (Ax + By = C):
To convert the equation to standard form, we need to ensure that the coefficients A, B, and C are integers, and A is positive.
6x - 8y = 8(x - 9) + 12
6x - 8y = 8x - 72 + 12
6x - 8y = 8x - 60
To simplify further, let's move all the terms to the left side:
6x - 8x - 8y = -60
-2x - 8y = -60
Now, multiply the entire equation by -1 to make the coefficient of x positive:
2x + 8y = 60
The equation is now in standard form, where A = 2, B = 8, and C = 60.