Complete the table to practice finding starting values in equations.

Question

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: \(y = 6x + 10\) | \(b = 10\) |