Question

Complete the table to practice finding starting values in equations.

The starting value in y=mx+b is the variable

*blank 1*

"y is 40 more than 5 times x"

"y is 3 more than twice the value of x"

y is 10 more than 6 multiplied by x

Equation: y = 5x + 40

Equation: y = 2x + 3

Equation: *blank 2*

b = 40

b = *blank 3*

b = *blank 4*



Options for blank 1

A m
B x
C b
D y

Options for blank 2

A y = (6 + 10) * x

B y = 10x + 6

C y = 6x + 10

Answer 1

Let's fill in the blanks step by step.

1. The starting value in the equation \(y = mx + b\) is represented by the variable \(b\) (the y-intercept). Therefore, for **blank 1**, the correct option is:
- **C b**

2. The phrase "y is 10 more than 6 multiplied by x" translates into the equation \(y = 6x + 10\). Therefore, for **blank 2**, the correct option is:
- **C y = 6x + 10**

3. In the equation \(y = 2x + 3\), the starting value (or the y-intercept \(b\)) is 3. Therefore, for **blank 3**, the correct answer is:
- **3**

4. For the third equation you provided, \(y = 6x + 10\), the starting value (or the y-intercept \(b\)) is 10. Therefore, for **blank 4**, the correct answer is:
- **10**

Putting it all together, the completed table would look like this:

| | Equation | b |
|-------------------|-----------------------------|-----|
| **blank 1** | | |
| | "y is 40 more than 5 times x" | |
| | "y is 3 more than twice the value of x" | |
| | "y is 10 more than 6 multiplied by x" | |
| | Equation: \(y = 5x + 40\) | \(b = 40\) |
| | Equation: \(y = 2x + 3\) | \(b = 3\) |
| **blank 2** | Equation: \(y = 6x + 10\) | \(b = 10\) |