Answer :
Certainly! To determine the equation of the line that best fits the given set of points [tex]\((x, y)\)[/tex], we need to find the slope ([tex]\(m\)[/tex]) and the y-intercept ([tex]\(c\)[/tex]) of this line. The points provided are:
[tex]\[ \begin{array}{c|c} x & y \\ \hline 0 & -6 \\ 1 & -10 \\ 2 & -14 \\ 3 & -18 \\ 4 & -22 \\ 5 & -26 \\ \end{array} \][/tex]
Step 1: Identify the slope (m).
The slope [tex]\(m\)[/tex] of the line can be found using the formula for a slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
However, since we are dealing with a set of points, it's easier and more accurate to use all points to find the best fit line. The slope [tex]\(m\)[/tex] has been determined to be approximately:
[tex]\[ m = -4.0 \][/tex]
Step 2: Identify the y-intercept (c).
The y-intercept [tex]\(c\)[/tex] can be found when [tex]\(x = 0\)[/tex], which means [tex]\(y = c\)[/tex]. This can also be derived from the equation of the line [tex]\(y = mx + c\)[/tex]. In this case, we use our known points. The y-intercept [tex]\(c\)[/tex] has been determined to be approximately:
[tex]\[ c = -6.0 \][/tex]
Step 3: Write the equation.
The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + c \][/tex]
Substituting the values of [tex]\(m\)[/tex] and [tex]\(c\)[/tex] into the equation, we get:
[tex]\[ y = -4x - 6 \][/tex]
Thus, the complete equation describing the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in the given set of points is:
[tex]\[ y = -4x - 6 \][/tex]
So the equation becomes:
[tex]\[ y = -4x - 6 \][/tex]
Therefore, [tex]\(y = -4x - 6\)[/tex].
[tex]\[ \begin{array}{c|c} x & y \\ \hline 0 & -6 \\ 1 & -10 \\ 2 & -14 \\ 3 & -18 \\ 4 & -22 \\ 5 & -26 \\ \end{array} \][/tex]
Step 1: Identify the slope (m).
The slope [tex]\(m\)[/tex] of the line can be found using the formula for a slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
However, since we are dealing with a set of points, it's easier and more accurate to use all points to find the best fit line. The slope [tex]\(m\)[/tex] has been determined to be approximately:
[tex]\[ m = -4.0 \][/tex]
Step 2: Identify the y-intercept (c).
The y-intercept [tex]\(c\)[/tex] can be found when [tex]\(x = 0\)[/tex], which means [tex]\(y = c\)[/tex]. This can also be derived from the equation of the line [tex]\(y = mx + c\)[/tex]. In this case, we use our known points. The y-intercept [tex]\(c\)[/tex] has been determined to be approximately:
[tex]\[ c = -6.0 \][/tex]
Step 3: Write the equation.
The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + c \][/tex]
Substituting the values of [tex]\(m\)[/tex] and [tex]\(c\)[/tex] into the equation, we get:
[tex]\[ y = -4x - 6 \][/tex]
Thus, the complete equation describing the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in the given set of points is:
[tex]\[ y = -4x - 6 \][/tex]
So the equation becomes:
[tex]\[ y = -4x - 6 \][/tex]
Therefore, [tex]\(y = -4x - 6\)[/tex].
Answer:
Step-by-step explanation:
\[ y = [?] x + \square \]
ChatGPT
To complete the equation
=
[
?
]
+
□
y=[?]x+□, you need the slope (the coefficient of
x) and the y-intercept (the constant term) of the linear equation. These are typically represented in the slope-intercept form of a linear equation
=
+
y=mx+b, where
m is the slope and
b is the y-intercept.
So, if you provide specific values or context, the equation will take the form:
=
+
y=mx+b
For example:
If the slope
m is 2 and the y-intercept
b is 3, the equation will be
=
2
+
3
y=2x+3.
If the slope
m is -1 and the y-intercept
b is 4, the equation will be
=
−
1
+
4
y=−1x+4.
Without additional information, the generic form is:
=
+
y=mx+b
