Convert to standard form (AX+BY=C)
1.y=3/2x+6
2. 2/3y=2x-5
3.7y-21=1/2x
4.-2/3x+3/4y=1
Convert to Slope/intercept form (y=mx+b)
1.3x-27=14
2.-9y-6x-18=0
3.8-2x+4y=0
12x=4y-8
I need help going through this because I am not sure if I am doing everything right and I also don't know how to use fractions. Thanks a million for all your help!
the best way to avoid fractions is to multiply through by the GCD.
#1. y = 3/2 x + 6
2y = 3x + 12
-3x + 2y = 12
or
3x-2y = -12
#2. -9y-6x-18 = 0
9y+6x+18 = 0
9y = -6x-18
y = -6/9 x - 18/9
y = -2/3 x - 2
A hood way to check is to pick a value for x, evaluate y, and see whether point satisfies the original equation.
Now, work the others the same way, and come on back if you get stuck. But show us whatcha got.
No problem! I'll guide you through each step to convert the given equations to the desired forms.
1. Convert to standard form (AX + BY = C):
The given equation is: y = (3/2)x + 6.
To convert it to standard form, we need to move all the terms to one side so that the equation is in the form AX + BY = C.
Start by multiplying each term by 2 to eliminate the fraction:
2y = 3x + 12.
Now, move the 3x term to the left side:
-3x + 2y = 12.
2. Convert to standard form (AX + BY = C):
The given equation is: (2/3)y = 2x - 5.
To eliminate the fraction, multiply every term by 3:
3 * (2/3)y = 3 * (2x - 5),
which simplifies to: 2y = 6x - 15.
Move the 6x term to the left side:
-6x + 2y = -15.
3. Convert to standard form (AX + BY = C):
The given equation is: 7y - 21 = (1/2)x.
To eliminate the fraction, multiply every term by 2:
2 * (7y - 21) = 2 * (1/2)x,
resulting in: 14y - 42 = x.
Rewriting the equation in the standard form:
-x + 14y = 42.
4. Convert to standard form (AX + BY = C):
The given equation is: (-2/3)x + (3/4)y = 1.
To get rid of the fractions, multiply every term by 12 (the least common multiple of 3 and 4):
12 * (-2/3)x + 12 * (3/4)y = 12 * 1,
which simplifies to: -8x + 9y = 12.
Now let's move on to converting the equations to slope-intercept form (y = mx + b):
1. Convert to slope-intercept form (y = mx + b):
The given equation is: 3x - 27 = 14.
To convert it to slope-intercept form, isolate y by moving the constant term (-27) to the right side:
3x = 14 + 27,
which simplifies to: 3x = 41.
To solve for x, divide both sides by 3:
x = 41/3.
Therefore, the equation in slope-intercept form is: y = 0x + 41/3, or simply y = 41/3.
2. Convert to slope-intercept form (y = mx + b):
The given equation is: -9y - 6x - 18 = 0.
Start by isolating y by moving the other terms to the right side:
-9y = 6x + 18.
Divide both sides by -9 to solve for y:
y = (-6/9)x - 18/9,
which simplifies to: y = (-2/3)x - 2.
3. Convert to slope-intercept form (y = mx + b):
The given equation is: 8 - 2x + 4y = 0.
Move the -2x term to the right side:
4y = 2x - 8.
Divide every term by 4 to solve for y:
y = (2/4)x - 8/4,
which simplifies to: y = (1/2)x - 2.
4. Convert to slope-intercept form (y = mx + b):
The given equation is: 12x = 4y - 8.
Start by moving the 4y term to the left side:
12x - 4y = -8.
To express y in terms of x, divide every term by 4:
-3x + y = -2.
I hope this step-by-step explanation and conversion helps! If you have any further questions, feel free to ask.