Answer: [tex]y=1.6x+6.8[/tex]
Step-by-step explanation:
1. The equation of a regression line has the following form:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
2. You need to calculate the slope with the points given in the exercise:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
3. Substitute values:
[tex]m=\frac{18-10}{7-2}[/tex]
[tex]m=\frac{8}{5}=1.6[/tex]
4. Now, you must calculate [tex]b[/tex]:
-Substitute the value of the slope into the equation above.
- Take one of the given points and substitute them into the equation.
Then:
[tex]y=mx+b\\10=(1.6)(2)+b\\b=10-3.2\\b=6.8[/tex]
5. Therefore, the equation is:
[tex]y=1.6x+6.8[/tex]
