Question

X

0

Determine some points on the line. Substitute x-values into the equation and calculate the y-values.

2x+3

Y

2(0) +3

3

2

2(2)+3

*blank*

3

*blank

*blank*

4

*blank

*blank*








A 11

B 2(5)+3

C 2(3)+3

D 9

E 2

F 13

G 2(4)+3

H 7

I 0

Fill in the blanks

Answer 1

To find the y-values for the line given by the equation \( y = 2x + 3 \), we can substitute the x-values into the equation.

Let's calculate the y-values for the specified x-values:

1. For \( x = 0 \):
\[
y = 2(0) + 3 = 0 + 3 = 3
\]
So, the first point is \( (0, 3) \).

2. For \( x = 2 \):
\[
y = 2(2) + 3 = 4 + 3 = 7
\]
So, the second point is \( (2, 7) \).

3. For \( x = 3 \):
\[
y = 2(3) + 3 = 6 + 3 = 9
\]
So, the third point is \( (3, 9) \).

4. For \( x = 4 \):
\[
y = 2(4) + 3 = 8 + 3 = 11
\]
So, the fourth point is \( (4, 11) \).

5. For \( x = 5 \):
\[
y = 2(5) + 3 = 10 + 3 = 13
\]
So, the fifth point is \( (5, 13) \).

Now we can fill in the blanks based on these calculations:

- The blank for \( 2(2) + 3 \) should be \( 7 \) (answer choice H).
- The blank for \( 2(3) + 3 \) should be \( 9 \) (answer choice D).
- The blank for \( 2(4) + 3 \) should be \( 11 \) (answer choice A).
- The blank for \( 2(5) + 3 \) should be \( 13 \) (answer choice F).

Here's the final filled-in information:

- For \( x = 2 \): \( 2(2) + 3 = 7 \) (Fill in: **7**)
- For \( x = 3 \): \( 2(3) + 3 = 9 \) (Fill in: **9**)
- For \( x = 4 \): \( 2(4) + 3 = 11 \) (Fill in: **11**)
- For \( x = 5 \): \( 2(5) + 3 = 13 \) (Fill in: **13**)

Thus, the answers for all the blanks are:

- For \( *blank* \) when \( x = 2 \): **7** (H)
- For \( *blank* \) when \( x = 3 \): **9** (D)
- For \( *blank* \) when \( x = 4 \): **11** (A)
- For \( *blank* \) when \( x = 5 \): **13** (F)