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a) Determine the equation of the straight line passing through the following points:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
y & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To determine the equation of the straight line passing through a set of points, you need to find the slope (m) and the y-intercept (b) of the line. The general form of the equation of a straight line is given by [tex]\( y = mx + b \)[/tex].

1. List the given points:
[tex]\[ (x,y) = \{(-3, 0), (-2, 1), (-1, 2), (0, 3), (1, 4), (2, 5), (3, 6)\} \][/tex]

2. Calculate the slope (m) and the y-intercept (b):

Using the given points, the slope [tex]\(m\)[/tex] and the y-intercept [tex]\(b\)[/tex] can be calculated using methods of linear regression or ordinary least squares fit. This approach finds the best-fitting straight line for the given set of points.

For the given points, the slope [tex]\(m\)[/tex] is approximately [tex]\(1.00\)[/tex] and the y-intercept [tex]\(b\)[/tex] is approximately [tex]\(3.00\)[/tex].

3. Write the equation of the line:

Substituting the values of the slope and y-intercept into the general form of the linear equation, we get:
[tex]\[ y = 1.00x + 3.00 \][/tex]

4. Summary:

Therefore, the equation of the straight line passing through the given points is:
[tex]\[ y = 1.00x + 3.00 \][/tex]
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