Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
y = 4x + 3
Step-by-step explanation:
Two lines are parallel if they have the same slope.
[tex]\\[/tex]
Let's say the line y = 4x + 5 is line 1.
Line 1 is in the form of y = mx + b (slope-intercept form)
where:
m = slope
b = y-intercept
[tex]\\[/tex]
Line 1 has a slope of 4. Let's say the slope of line 1 is m₁
[tex]\\[/tex]
The problem says the we need to find a line that is parallel to line 1 and passing through point (2, 11). Let's say the line we want to find is Line 2 and it's slope is m₂.
[tex]\\[/tex]
Since line 1 and line 2 are parallel, their slope is the same, m₁ = m₂.
m₂ = 4
[tex]\\[/tex]
Since line 2 is passing through a point, we can use the point-slope form of a line to determine the equation of the line.
Point-slope form of a line:
[tex]\mathsf{y-y_1=m(x-x_1)}[/tex]
where:
y₁ = y coordinate of the point
x₁ = x coordinate of the point
m = slope of the line
[tex]\\[/tex]
For the line 2, the coordinates of the point is (2, 11). x₁ = 2 and y₁ = 11.
Substituting all the values we have in the point-slope form:
[tex]\mathsf{y-11=4(x-2)}[/tex]
simplifying the equation and converting it to slope-intercept form
[tex]\mathsf{y-11=4x-8}[/tex]
[tex]\mathsf{y=4x-8+11}[/tex]
[tex]\mathsf{y=4x+3} \longleftarrow \textsf{\textbf{ANSWER}}[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.