Answer:
Using the point-slope form:
The equation of the line is given by:
[tex]y-y_1 =m(x-x_1)[/tex] .....[1] where
m is the slope of the line and [tex](x_1, y_1)[/tex] is the point on the line.
As per the statement:
Given: Two points i,e (34, 76) and (42, 91)
First calculate slope(m):
Slope is given by:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we have;
[tex]\text{Slope (m)} = \frac{91-76}{42-34}=\frac{15}{8}=1.875[/tex]
Now, substitute the value of m and (34, 76) in [1] we have;
[tex]y-76 =1.875(x-34)[/tex]
Using distributive property: [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
[tex]y-76 =1.875x-63.75[/tex]
Add 76 to both sides we get;
[tex]y=1.875x+76[/tex]
Therefore, the equation of the trend line is: [tex]y=1.875x+76[/tex]
Answer:
The equation of the trend line is [tex]y=1.875x+12.25[/tex].
Step-by-step explanation:
Given : The points (34,76) (42,91).
To find : The equation of the trend line (line of best fit) ?
Solution :
Using two point slope form to find the equation of line.
[tex](y-y_1)=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)[/tex]
Here, [tex](x_1,y_1)=(34,76)[/tex] and [tex](x_2,y_2)=(42,91)[/tex]
Substitute the value,
[tex](y-76)=(\frac{91-76}{42-34})(x-34)[/tex]
[tex](y-76)=(\frac{15}{8})(x-34)[/tex]
[tex](y-76)=\frac{15}{8}x-\frac{15}{8}\times 34[/tex]
[tex](y-76)=1.875x-63.75[/tex]
[tex]y=1.875x-63.75+76[/tex]
[tex]y=1.875x+12.25[/tex]
Therefore, the equation of the trend line is [tex]y=1.875x+12.25[/tex].
