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.
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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 \( y = -2x + 1.5 \).
- 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).