Respuesta :
Preparations
In order to solve this problem, we need a few formulas to help us get to the answer:
The first formula we need is the Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are two different points.
The second formula we need is Point-Slope Form:
[tex]\displaystyle y - y_0 = m(x - x_0)[/tex]
where (x₀, y₀) is a given point on the line and m is the slope.
Defining
Now, we can organize and define what the problem has given us:
We are first given information that a line passes through the points (6, 2) and (2, 4).
We are also given that the parallel line passes through (-1, 6).
Work
Let's first find the slope of the line that passes through two points:
[tex]\displaystyle\begin{aligned}m & = \frac{4 - 2}{2 - 6} \\& = \frac{2}{-4} \\& = \boxed{ - \frac{1}{2} } \\\end{aligned}[/tex]
∴ we know that the slope is equal to negative one-half.
Let's substitute in our slope into Point-Slope Form since parallel lines have the same slope:
[tex]\displaystyle y - y_0 = m(x - x_0) \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0)[/tex]
Recall that we were given the initial point (-1, 6). Let's also substitute this into Point-Slope Form:
[tex]\displaystyle \begin{aligned}y - y_0 = m(x - x_0) & \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0) \\& \Rightarrow y - 6 = - \frac{1}{2} (x - -1) \\& \Rightarrow \boxed{ y - 6 = -\frac{1}{2}(x + 1) } \\\end{aligned}[/tex]
Answer
∴ we have found that the point-slope form of the equation of a line that passes through the point (-1, 6) and is parallel to the line that passes through the points (6, 2) and (2, 4) is equal to:
[tex]\displaystyle \boxed{ y - 6 = -\frac{1}{2}(x + 1) }[/tex]
Hope this helps!
#Brainlystudentskeeponlearning
___
Learn more about writing equations: https://brainly.com/question/9972577
Learn a little more about Algebra here: https://brainly.com/question/17011730
Hey, while you're at it, why not take a sneak peak of higher-level math here?: https://brainly.com/question/28758158
Answer:
The first formula we need is the Slope Formula:
where (x₁, y₁) and (x₂, y₂) are two different points.
The second formula we need is Point-Slope Form:
where (x₀, y₀) is a given point on the line and m is the slope.
Defining
Now, we can organize and define what the problem has given us:
We are first given information that a line passes through the points (6, 2) and (2, 4).
We are also given that the parallel line passes through (-1, 6).
Work
Let's first find the slope of the line that passes through two points:
∴ we know that the slope is equal to negative one-half.
Let's substitute in our slope into Point-Slope Form since parallel lines have the same slope:
Recall that we were given the initial point (-1, 6). Let's also substitute this into Point-Slope Form:
Answer
∴ we have found that the point-slope form of the equation of a line that passes through the point (-1, 6) and is parallel to the line that passes through the points (6, 2) and (2, 4) is equal to:
