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]
