Give me some math problems with answers: turning something into y=mx+b

Here are some math problems that involve converting linear equations into the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:

---

### Problem 1:
Convert the following equation into slope-intercept form:

\[
2x + 3y = 12
\]

#### Solution:
1. Subtract \( 2x \) from both sides:
   \[
   3y = -2x + 12
   \]

2. Divide both sides by 3:
   \[
   y = -\frac{2}{3}x + 4
   \]

So, the equation in slope-intercept form is:
\[
y = -\frac{2}{3}x + 4
\]

---

### Problem 2:
Convert the following equation into slope-intercept form:

\[
4x - 2y = 10
\]

#### Solution:
1. Subtract \( 4x \) from both sides:
   \[
   -2y = -4x + 10
   \]

2. Divide both sides by -2:
   \[
   y = 2x - 5
   \]

So, the equation in slope-intercept form is:
\[
y = 2x - 5
\]

---

### Problem 3:
Convert the following equation into slope-intercept form:

\[
5y - 10x = 15
\]

#### Solution:
1. Add \( 10x \) to both sides:
   \[
   5y = 10x + 15
   \]

2. Divide both sides by 5:
   \[
   y = 2x + 3
   \]

So, the equation in slope-intercept form is:
\[
y = 2x + 3
\]

---

### Problem 4:
Convert the following equation into slope-intercept form:

\[
6x + y = 8
\]

#### Solution:
1. Subtract \( 6x \) from both sides:
   \[
   y = -6x + 8
   \]

So, the equation in slope-intercept form is:
\[
y = -6x + 8
\]

---

### Problem 5:
Convert the following equation into slope-intercept form:

\[
3x + 4y = -20
\]

#### Solution:
1. Subtract \( 3x \) from both sides:
   \[
   4y = -3x - 20
   \]

2. Divide both sides by 4:
   \[
   y = -\frac{3}{4}x - 5
   \]

So, the equation in slope-intercept form is:
\[
y = -\frac{3}{4}x - 5
\]

---

Would you like further details on any of these examples, or have any specific questions?

### Relative Questions:
1. How do you find the slope when the equation is not in standard form?
2. What is the significance of the y-intercept in graphing?
3. How can you rewrite an equation if it has fractions in the slope?
4. What happens if both the slope and y-intercept are negative?
5. Can a vertical line equation be expressed in the form \( y = mx + b \)?

### Tip:
Always isolate the \( y \)-term first when converting equations into slope-intercept form!

Explore how to convert linear equations into the slope-intercept form y=mx+b. This guide provides step-by-step solutions to problems, covering essential algebra concepts like slopes, y-intercepts, and equation rearrangement. Suitable for Grades 8-10.

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