To solve the problem we must know about the equation of a line.
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.
The equation of the trend line is N = -2M+110.
If we look at the image given below we will find out that the line is going through a few points,
(20,70), (25,60)
We can write the point in the form (x, y),
Point 1= [tex](x_1, y_1)[/tex] = (20, 70)
Point 2= [tex](x_2, y_2)[/tex] = (25, 60)
We know the general equation for a line, therefore,
y = mx+c
where m is the slope and c is the constant.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values we get,
[tex]m=\dfrac{60-70}{25-20} = \dfrac{-10}{5}=-2[/tex]
Thus, the slope of the trend line is negative and is equal to 2.
For Point 1,
y = mx+c
Substitute the value,
[tex]y_1 = mx_1+c\\70 = -2(20)+c\\70=-40+c\\70+40=c\\110=c[/tex]
Thus, the value of the constant is 110.
y = mx+c
Substituting the values,
N = -2M+110
Hence, the equation of the trend line is N = -2M+110.
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