Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
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:
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
