Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer:
[tex]y=\dfrac{1}{2}x-4[/tex]
Step-by-step explanation:
Perpendicular Lines
Lines that form a 90-degree angle between each other have slopes that are negative reciprocals to each other.
For example,
Line A has a slope of [tex]\dfrac{1}{4}[/tex], so line B's slope is -4.
A more algebraic way of finding the negative reciprocal is,
[tex]-\dfrac{1}{m}[/tex],
where m is line A's slope --or any line's slope.
Finding the Equation of a Line
When given a point on the line, it can be plugged into the linear equation and rearranged to find its m or b value, depending on whether either of the values is known already.
[tex]\hrulefill[/tex]
Solving the Problem
If our equation is perpendicular to a line with a slope of -2, then our equation's m value must be [tex]-\dfrac{1}{-2 } =\dfrac{1}{2}[/tex].
So, our equation is currently,
[tex]y=\dfrac{1}{2}x+b[/tex].
To find the b value we can plug in the given coordinate point,
[tex]-7=\dfrac{1}{2}(-6)+b[/tex]
[tex]-7=-3+b[/tex]
[tex]-4=b[/tex].
So our final answer is,
[tex]y=\dfrac{1}{2}x-4[/tex].
y = (1/2)x - 4 is the equation of the perpendicular line.
The equation of the perpendicular line:
- Slope of the given line: The given line is in slope-intercept form (y = -2x + 4). The slope of this line is -2.
- Slope of the perpendicular line: The slope of a line perpendicular to another line is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is 1/2.
- Point-slope form: We know a point the perpendicular line must pass through (-6, -7) and its slope is 1/2. We can use the point-slope form of linear equations: y - y₁ = m(x - x₁)
where:
y is the y-coordinate of any point on the line
y₁ is the y-coordinate of the known point (-7)
m is the slope (1/2)
x is the x-coordinate of any point on the line
x₁ is the x-coordinate of the known point (-6)
Substitute and solve for y:
y - (-7) = (1/2) (x - (-6))
y + 7 = (1/2)x + 3
Slope-intercept form:
Isolate y to get the equation in slope-intercept form (y = mx + b):
y = (1/2)x + 3 - 7
y = (1/2)x - 4.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
