Question

What is a point on the line represented by the equation y−3.5=−2(x+1)?

(−1, 3.5)

(−3.5, 1)

(1, −3.5)

(3.5, −1)

Answer 1

To find a point on the line represented by the equation \( y - 3.5 = -2(x + 1) \), we will simplify this equation and determine if any of the given points satisfy it.

1. Start by rewriting the equation in slope-intercept form (y = mx + b):

\[
y - 3.5 = -2(x + 1)
\]
\[
y - 3.5 = -2x - 2
\]
\[
y = -2x - 2 + 3.5
\]
\[
y = -2x + 1.5
\]

Now, we have the equation of the line in the form \( y = -2x + 1.5 \).

2. Next, we will check each of the given points to see if they satisfy the equation:

**Point (−1, 3.5)**:
- Substitute \( x = -1 \) into the equation:
\[
y = -2(-1) + 1.5 = 2 + 1.5 = 3.5
\]
This point satisfies the equation.

**Point (−3.5, 1)**:
- Substitute \( x = -3.5 \) into the equation:
\[
y = -2(-3.5) + 1.5 = 7 + 1.5 = 8.5
\]
This point does not satisfy the equation.

**Point (1, −3.5)**:
- Substitute \( x = 1 \) into the equation:
\[
y = -2(1) + 1.5 = -2 + 1.5 = -0.5
\]
This point does not satisfy the equation.

**Point (3.5, −1)**:
- Substitute \( x = 3.5 \) into the equation:
\[
y = -2(3.5) + 1.5 = -7 + 1.5 = -5.5
\]
This point does not satisfy the equation.

From the evaluations above, the only point that lies on the line is:

**(−1, 3.5)**.