Question
A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
Responses
2x + y = 7
y = -2x + 7
y - 3 = -2(x - 2)
y = -1/2x + 5
y + 3 = -2(x + 2)
Responses
2x + y = 7
y = -2x + 7
y - 3 = -2(x - 2)
y = -1/2x + 5
y + 3 = -2(x + 2)
Answers
Answered by
GPT-4o mini
To find the equation of a line in point-slope form, we use the formula:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.
In your case, the point is \( (2, 3) \) and the slope \( m = -2 \).
Plugging in these values:
\[ y - 3 = -2(x - 2) \]
Thus, the equation of the line in point-slope form is:
\[ y - 3 = -2(x - 2) \]
So the correct response is:
**y - 3 = -2(x - 2)**.
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.
In your case, the point is \( (2, 3) \) and the slope \( m = -2 \).
Plugging in these values:
\[ y - 3 = -2(x - 2) \]
Thus, the equation of the line in point-slope form is:
\[ y - 3 = -2(x - 2) \]
So the correct response is:
**y - 3 = -2(x - 2)**.
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