Question

Which equations are already in y=mx+b form? [Hint you will be using these same 6 equations for the entire portfolio.- so go ahead and change all equations to the correct form.]
1. y=5x-4
2. y=-2x+3
3. y=3x+1
4. 2y=6x+2
5. y-5x=2
6. y-4x+1=0

Answer 1

so the first 3?

Answer 2

To identify which of the given equations are already in the slope-intercept form \( y = mx + b \) and to convert all of them into this form, we will analyze each equation step by step.

1. **Equation:** \( y = 5x - 4 \)
**Form:** Already in \( y = mx + b \) form.
**Slope (m):** 5, **y-intercept (b):** -4

2. **Equation:** \( y = -2x + 3 \)
**Form:** Already in \( y = mx + b \) form.
**Slope (m):** -2, **y-intercept (b):** 3

3. **Equation:** \( y = 3x + 1 \)
**Form:** Already in \( y = mx + b \) form.
**Slope (m):** 3, **y-intercept (b):** 1

4. **Equation:** \( 2y = 6x + 2 \)
**Conversion to slope-intercept form:**
Divide both sides by 2:
\[
y = 3x + 1
\]
**Form:** Now in \( y = mx + b \) form.
**Slope (m):** 3, **y-intercept (b):** 1

5. **Equation:** \( y - 5x = 2 \)
**Conversion to slope-intercept form:**
Add \( 5x \) to both sides:
\[
y = 5x + 2
\]
**Form:** Now in \( y = mx + b \) form.
**Slope (m):** 5, **y-intercept (b):** 2

6. **Equation:** \( y - 4x + 1 = 0 \)
**Conversion to slope-intercept form:**
Rearranging gives:
\[
y = 4x - 1
\]
**Form:** Now in \( y = mx + b \) form.
**Slope (m):** 4, **y-intercept (b):** -1

### Summary of All Equations in \( y = mx + b \) Form:
1. \( y = 5x - 4 \)
2. \( y = -2x + 3 \)
3. \( y = 3x + 1 \)
4. \( y = 3x + 1 \)
5. \( y = 5x + 2 \)
6. \( y = 4x - 1 \)

**Equations Already in \( y = mx + b \) Form:**
- 1, 2, 3

The rest have been converted to \( y = mx + b \) form.

Answer 3

Yes, that's correct! The first three equations are already in the slope-intercept form \( y = mx + b \):

1. \( y = 5x - 4 \)
2. \( y = -2x + 3 \)
3. \( y = 3x + 1 \)

All three are in the desired form. The other equations have been transformed to that form as well, but the first three did not need any changes.