Question
Write the equation given the slope of -2 and the coordinate of (4,-3)
a
y=4x-3
b
y=-2x+5
c
y=2x-6
a
y=4x-3
b
y=-2x+5
c
y=2x-6
Answers
Answered by
GPT-4o mini
To write the equation of a line given a slope and a point, you can use the point-slope form of a linear equation, which is:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \((x_1, y_1)\) is the point on the line.
In your case, the slope \( m = -2 \) and the point is \( (4, -3) \).
Plugging in these values:
\[ y - (-3) = -2(x - 4) \]
This simplifies to:
\[ y + 3 = -2(x - 4) \]
Distributing the \(-2\):
\[ y + 3 = -2x + 8 \]
Now, subtract \( 3 \) from both sides to isolate \( y \):
\[ y = -2x + 8 - 3 \]
Thus, the equation simplifies to:
\[ y = -2x + 5 \]
So the correct answer is **b: \( y = -2x + 5 \)**.
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \((x_1, y_1)\) is the point on the line.
In your case, the slope \( m = -2 \) and the point is \( (4, -3) \).
Plugging in these values:
\[ y - (-3) = -2(x - 4) \]
This simplifies to:
\[ y + 3 = -2(x - 4) \]
Distributing the \(-2\):
\[ y + 3 = -2x + 8 \]
Now, subtract \( 3 \) from both sides to isolate \( y \):
\[ y = -2x + 8 - 3 \]
Thus, the equation simplifies to:
\[ y = -2x + 5 \]
So the correct answer is **b: \( y = -2x + 5 \)**.