Answer :
Answer:
y = 2x + 7.
Step-by-step explanation:
The slope of the blue line is $-\dfrac{1}{2}$ (negative reciprocal of $-\dfrac{1}{2}$ is $2$ ). Lines are considered perpendicular if their slopes are negative reciprocals of each other. So, the perpendicular line will have a slope of $2$ and it will pass through the point $(-4, 1)$.
Since the slope of the perpendicular line is $2$ and it passes through $(-4, 1)$, we can use the point-slope form of linear equations to find the equation:
y - y_1 = m(x - x_1)
where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through. Plugging in $m = 2$, $x_1 = -4$, and $y_1 = 1$, we get:
y - 1 = 2(x - (-4))
Simplifying the right side:
y - 1 = 2x + 8
y = 2x + 7
Therefore, the equation of the line perpendicular to y = -1/2x+3 and passing through (-4,1) is y = 2x + 7.
Answer:
To find the equation of a line perpendicular to \( y = -\frac{1}{2}x + 3 \) and passing through the point \((-4, 1)\), follow these steps:
1. **Determine the slope of the perpendicular line:**
- The slope of the given line is \(-\frac{1}{2}\).
- The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m \) of the perpendicular line is:
\[
m = -\left(-\frac{1}{2}\right)^{-1} = 2
\]
2. **Use the point-slope form of the line equation:**
The point-slope form of the equation of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
Here, \( (x_1, y_1) = (-4, 1) \) and \( m = 2 \).
3. **Substitute the values into the point-slope form:**
\[
y - 1 = 2(x + 4)
\]
4. **Simplify to get the equation in slope-intercept form:**
\[
y - 1 = 2x + 8
\]
\[
y = 2x + 9
\]
Therefore, the equation of the line perpendicular to \( y = -\frac{1}{2}x + 3 \) and passing through the point \((-4, 1)\) is:
\[
y = 2x + 9
\]
Step-by-step explanation:
