Given the table:
Hours worked Account Earned
3 $34.50
5 $57.50
8 $92.90
From the data given in the table, let's write an equation that can be used to determine the amount of money Nina earns given the number of hours she worked.
Apply the slope-intecept formula:
y = mx + b
WHere:
m is the slope
b is the y-intercept.
To find the slope, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points from the table:
(x1, y1) ==> (3, 34.50)
(x2, y2) ==> (5, 57.50)
Thus, we have:
[tex]\begin{gathered} m=\frac{57.50-34.50}{5-3} \\ \\ m=\frac{23}{2} \\ \\ m=11.5 \end{gathered}[/tex]Here, the slope is:
m = 11.5
To find the y-intercept b, input the value of m and substitute one point for the values of x and y in (y=mx+b)
Take the point: (3, 34.50)
[tex]\begin{gathered} y=mx+b \\ \\ 34.50=11.5(3)+b \\ \\ 34.5=34.5+b \\ \\ b=34.5-34.5 \\ \\ b=0 \end{gathered}[/tex]Therefore, the equation is:
[tex]y=11.5x[/tex]Where:
y represents the amount earned
x represents the number of hours worked.
ANSWER:
y = 11.5x