A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the trend line is y=(4/7)x+(1/7).
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The equation of a line is given by,
y =mx + c
where,
- x is the coordinate of the x-axis,
- y is the coordinate of the y-axis,
- m is the slope of the line, and
- c is constant.
As we can see that the graph is a straight line. And the line has 2 points A at (5,3) and B at (12,7). Therefore, the slope of the line can be written as,
[tex]\text{Slope of line}=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{7-3}{12-5}=\dfrac{4}{7}[/tex]
Now, if we substitute the value of point A and the slope of the line in the general equation of the line. It will be written as,
[tex]y=\dfrac47x+c\\\\3=\dfrac47(5)+c\\\\3=\dfrac{20}{7}+c\\c=3-\dfrac{20}{7}\\c=\dfrac{1}{7}[/tex]
Thus, the equation of the trend line is y=(4/7)x+(1/7).
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