Answer:
y = 10x + 50
Step-by-step explanation:
To determine the equation of the line of fit from the scatter plot data, we need to use the coordinates of two points that the line passes through. Given points are (0, 50) and (2, 70).
1. Find the slope (m):
The formula for the slope [tex] \sf m [/tex] is:
[tex] \sf m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using the points [tex] \sf (0, 50) [/tex] and [tex] \sf (2, 70) [/tex]:
[tex] \sf m = \frac{70 - 50}{2 - 0} = \frac{20}{2} = 10 [/tex]
2. Determine the y-intercept ([tex] \sf b [/tex]):
The equation of a line in slope-intercept form is:
[tex] \sf y = mx + b [/tex]
Using the point [tex] \sf (0, 50) [/tex]:
[tex] \sf 50 = 10 \cdot 0 + b \implies b = 50 [/tex]
3. Write the equation of the line:
Substitute the slope [tex] \sf m [/tex] and y-intercept [tex] \sf b [/tex] into the slope-intercept form:
[tex] \sf y = 10x + 50 [/tex]
Thus, the equation of the line of fit is: