Question
Write the equation given a slope of -1 and the coordinate (6,-3)
a
y=-x+3
b
y=2x-5
c
y=x-6
a
y=-x+3
b
y=2x-5
c
y=x-6
Answers
GPT-4o mini
To find the equation of a line with a slope of -1 that passes through the point (6, -3), we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the given point.
In this case, \( m = -1 \), \( x_1 = 6 \), and \( y_1 = -3 \).
Substituting these values into the equation:
\[ y - (-3) = -1(x - 6) \]
\[ y + 3 = -1(x - 6) \]
\[ y + 3 = -x + 6 \]
\[ y = -x + 6 - 3 \]
\[ y = -x + 3 \]
So the equation of the line is:
\[ y = -x + 3 \]
Therefore, the correct answer is:
**a. y = -x + 3**
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the given point.
In this case, \( m = -1 \), \( x_1 = 6 \), and \( y_1 = -3 \).
Substituting these values into the equation:
\[ y - (-3) = -1(x - 6) \]
\[ y + 3 = -1(x - 6) \]
\[ y + 3 = -x + 6 \]
\[ y = -x + 6 - 3 \]
\[ y = -x + 3 \]
So the equation of the line is:
\[ y = -x + 3 \]
Therefore, the correct answer is:
**a. y = -x + 3**