Solution-
Here,
x = number of years worked,
y = salary in dollars.
Tom is getting $75,000 of salary right now, so for this case,
x₁ = 0,
y₁ = 75000
Tom will be getting a salary of $83,000 after 4 years from now, so for this case,
x₂ = 4,
y₂ = 83000
1.
Rate of change of salary = slope of the line joining (x₁, y₁), ( x₂, y₂)
[tex]Slope= \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\Rightarrow Slope= \frac{83000-75000}{4-0}[/tex]
[tex]\Rightarrow Slope=2000[/tex]
∴ The salary increase per year is $2000.
2.
Equation of the line in slope-intercept formula,
[tex]y-y_1=m(x-x_1)[/tex]
Putting x₁ = 0, y₁ = 75000, we get
[tex]y-75000=2000(x-0)[/tex]
[tex]y-75000=2000x[/tex]
[tex]y=75000+2000x[/tex]
3.
Putting x = 10, we can compute the value of y to get the salary after 10 years.
[tex]y=75000+2000(10)[/tex]
[tex]y=75000+20000[/tex]
[tex]y=95000[/tex]
∴ Tom's salary in ten years will be $95,000
Answer:
[tex]y_{0}=75,000[/tex] when x=0.
[tex]y_{4}=83,000[/tex] when x=4.
1.Rate of change=[tex]Slope=\frac{y_{4}- y_{0}}{4-0}\\\\= \frac{83,000-75,000}{4-0}\\\\=\frac{8,000}{4}\\\\=2000[/tex]
2. Slope intercept form of salary and number of years
[tex]\frac{y-75,000}{x-0}=2000[/tex] →[as slope =2,000]
→y-75,000=2,000 x
→y= 2000 x+ 75,000
3.Tom salary after 10 years ,
put x=10
y=2000×10+75,000
y=20,000+75,000
y=$95,000
Salary after 10 years=$95,000
