Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
