Question

Convert Each Equation To Slope-Intercept Form. (1/2)

1. y + 3 = 4(x + 6)

2. 6x + 2y = 12

3. y = -2 + 1/3(x + 9)

4. 2x - 5y = -15

5. -x - 2y = 2

Answer 1

Hey there, Mandoguy!

To convert each equation to slope-intercept form, first we need to distribute everything that's on the parenthesis (if it has one)
So, number one would be

1) y + 3 = 4x + 24 (I multiplied 4 times x and 4 times 6)
Now, we need to isolate y and since they are adding 3 to it, we need to subtract 3 to cancel it out. Remember what we do on one side we have to do it in the other side.
So, it would be y + 3 - 3 = 4x + 24 - 3
Number 1 would be
y = 4x + 21
$y=4x+21$

2) 6x + 2y = 12
Goes to
2y = 12 - 6x (I subtracted 6x from both sides to leave 2y alone)
y = 6 - 3x (I divided both sides by 2 since y it's being multiplied by 2)
y = -3x + 6 (Now, I just rearranged to make it y = mx + b
$y=-3x+6$

3) y = -2 + 1/3 (x + 9) In this case y is already isolated but we have parenthesis and we can't have that.
So, we distribute the number that's in front of the parenthesis to the numbers inside.
y = -2 + 1/3x + 3 (I multiplied 1/3 times x and 1/3 times 9 which is 3)
y = 1/3x + 1 (I combined like terms and rearranged to make it y=mx+b)
$y= \frac{1}{3} x+1$

4) 2x - 5y = -15 (Same as always. Isolate y. Subtract 2x from both sides)
-5y = -15 - 2x (Did you see that? We have a negative value on y and we can't have that. To fix it, we multiply both sides by -1 or just change the sign of every term)
Once you do that you will get
5y = 15 + 2x
y = 3 + 2/5 x (I divided both sides by 5 to isolate y)
y = 2/5x + 3 (Rearranged it to y = mx + b)
$y = \frac{2}{5}x + 3$

5) -x - 2y = 2 (Since the x it's being subtracted, we added to both sides)
-2y = 2 + x (See again? We have a negative value on y, so we multiply by -1 on both sides or change every sign to the opposite of itself)
So we get
2y = -2 - x (Now, we divide both sides by 2 to isolate y)
y = -1/2x - 1 (Rearranged to y = mx + b)
$y = - \frac{1}{2} x - 1$

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