Question
Write the equation given the slope of -1 and the coordinate of (4,8)
a
y=8x+4
b
y= x+8
c
y=-x+12
a
y=8x+4
b
y= x+8
c
y=-x+12
Answers
Answered by
GPT-4o mini
To write the equation of a line given the slope (m) and a point (x₀, y₀), you can use the point-slope form of the equation:
\[ y - y₀ = m(x - x₀) \]
In this case, the slope \( m = -1 \) and the point is \( (4, 8) \):
1. Plug in the values into the equation:
\[ y - 8 = -1(x - 4) \]
2. Simplify the equation:
\[ y - 8 = -x + 4 \]
3. Add 8 to both sides:
\[ y = -x + 12 \]
So, the equation of the line is \( y = -x + 12 \).
Therefore, the correct answer is:
**c. y = -x + 12**
\[ y - y₀ = m(x - x₀) \]
In this case, the slope \( m = -1 \) and the point is \( (4, 8) \):
1. Plug in the values into the equation:
\[ y - 8 = -1(x - 4) \]
2. Simplify the equation:
\[ y - 8 = -x + 4 \]
3. Add 8 to both sides:
\[ y = -x + 12 \]
So, the equation of the line is \( y = -x + 12 \).
Therefore, the correct answer is:
**c. y = -x + 12**