Consider the individual graph.
1)
Given:
We get the points (0,2) and (7,3) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]
Substitute x =7 and y =3 in the equation to find the value of m.
[tex]3=m(7)+2[/tex]
Solve for m.
[tex]3-2=7m[/tex][tex]m=\frac{1}{7}[/tex]
Substitute m=1/7 and b =2 in the line equation.
[tex]y=\frac{1}{7}x+2[/tex]
Answer:
[tex]y=\frac{1}{7}x+2[/tex]
2)
Given:
We get the points (0,2) and (7,6) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]
Substitute x =7 and y =6 in the equation to find the value of m.
[tex]6=m(7)+2[/tex]
Solve for m.
[tex]6-2=7m[/tex][tex]m=\frac{4}{7}[/tex]
Substitute m=4/7and b =2 in the line equation.
[tex]y=\frac{4}{7}x+2[/tex]
Answer:
[tex]y=\frac{4}{7}x+2[/tex]
3)
Given:
We get the points (0,2) and (7,1) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]
Substitute x =7 and y =1 in the equation to find the value of m.
[tex]1=m(7)+2[/tex]
Solve for m.
[tex]1-2=7m[/tex][tex]m=\frac{-1}{7}[/tex]
Substitute m= -1/7and b =2 in the line equation.
[tex]y=\frac{-1}{7}x+2[/tex]
Answer:
[tex]y=\frac{-1}{7}x+2[/tex]
4)
Given:
We get the points (0,2) and (6.7) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]
Substitute x =6 and y =7 in the equation to find the value of m.
[tex]7=m(6)+2[/tex]
Solve for m.
[tex]7-2=6m[/tex][tex]m=\frac{5}{6}[/tex]
Substitute m= 5/6 and b =2 in the line equation.
[tex]y=\frac{5}{6}x+2[/tex]
Answer:
[tex]y=\frac{5}{6}x+2[/tex]
[tex]y=\frac{5}{6}x+2[/tex]
