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.]

Question

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

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 2

so the first 3?

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.