Answer:
1.
- Gabe earns 13.5 per hour
2.
x ------------------ 4 ---- 8 --------- 12 ------ 16
Earnings ----- 57 ---- 111 ------- 165------ 219
Step-by-step explanation:
See attachment for complete question
Solving (a): Gabe's earnings per hour,
To do this, we simply calculate the slope (m) of the table.
[tex]m = \frac{y_2 - y_1}{x_2- x_1}[/tex]
Where
[tex](x_1,y_1) = (3,40.5)[/tex]
[tex](x_2,y_2) = (6,81.0)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2- x_1}[/tex]
[tex]m = \frac{81 - 40.5}{6 - 3}[/tex]
[tex]m = \frac{40.5}{3}[/tex]
[tex]m = 13.5[/tex]
Hence, Gabe earns 13.5 per hour
Solving (b): Jordan earnings
First, we calculate the equation of Gabe's table using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 13.5[/tex] and [tex](x_1,y_1) = (3,40.5)[/tex]
[tex]y - 40.5 = 13.5(x - 3)[/tex]
[tex]y - 40.5 = 13.5x - 40.5[/tex]
[tex]y = 13.5x[/tex]
If Jordan earns 3 more per hour than Gabe, then: Jordan's equation would be;
[tex]y = 13.5x + 3[/tex]
When x = 4
[tex]y = 13.5*4 + 3 = 54 + 3 = 57[/tex]
When x = 8
[tex]y = 13.5*8 + 3 = 108 + 3 = 111[/tex]
When x = 12
[tex]y = 13.5*12 + 3 = 162 + 3 = 165[/tex]
When x = 16
[tex]y = 13.5*16 + 3 = 216 + 3 = 219[/tex]
