Answer:
[tex]y=15x[/tex]
Step-by-step explanation:
Let
x ----> the time
y ----> the distance
we have the points
[tex](1,15),(2,30),(4,60),(6,90)[/tex]
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
[tex](1,15),(6,90)[/tex]
substitute in the formula
[tex]m=\frac{90-15}{6-1}[/tex]
[tex]m=\frac{75}{5}[/tex]
[tex]m=15[/tex]
Find the linear equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=15[/tex]
[tex]point\ (1,15)[/tex]
substitute
[tex]y-15=15(x-1)[/tex] ---> equation in point slope form
Convert to slope intercept form
[tex]y-15=15x-15[/tex]
[tex]y=15x-15+15[/tex]
[tex]y=15x[/tex]
Verify for x=2
[tex]y=15(2)=30[/tex] ----> is ok in the table
Verify for x=4
[tex]y=15(4)=60[/tex] ----> is ok in the table
