Question

What is a point on the line represented by the equation y−5.5=
4
1
​
(x+2)?

(5.5, −2)

(−5.5, 2)

(2, −5.5)

(−2, 5.5)

Answer 1

To find a point that lies on the line represented by the equation \( y - 5.5 = \frac{4}{1}(x + 2) \), we can first simplify the equation.

The equation can be rewritten as:

\[
y - 5.5 = 4(x + 2)
\]
\[
y - 5.5 = 4x + 8
\]
\[
y = 4x + 8 + 5.5
\]
\[
y = 4x + 13.5
\]

Now we will check each of the provided points to see if they satisfy this equation.

1. For the point **(5.5, -2)**:
\[
y = -2
\]
\[
4(5.5) + 13.5 = 22 + 13.5 = 35.5 \quad (\text{not } -2)
\]

2. For the point **(-5.5, 2)**:
\[
y = 2
\]
\[
4(-5.5) + 13.5 = -22 + 13.5 = -8.5 \quad (\text{not } 2)
\]

3. For the point **(2, -5.5)**:
\[
y = -5.5
\]
\[
4(2) + 13.5 = 8 + 13.5 = 21.5 \quad (\text{not } -5.5)
\]

4. For the point **(-2, 5.5)**:
\[
y = 5.5
\]
\[
4(-2) + 13.5 = -8 + 13.5 = 5.5 \quad (\text{is } 5.5)
\]

The point that satisfies the equation \( y = 4x + 13.5 \) is **(-2, 5.5)**.

Thus, the answer is:

\[
\boxed{(-2, 5.5)}
\]