Tom has just received a new job offer he is told that his salary will be 75,000.00 per year he is also told that his salary will probably be 83,000.00 in four years assume that y= toms salary amount in dollars and x= the number of years worked 1. use data given to find rate of change, or the salary increase per year (hint: commute the slope.) 2. use data given and the slope vale from step 1 to write the slope- intercept form of the line. 3. based on your equation from step 2 what will toms salary be in ten years?

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)

∴ The salary increase per year is $2000.

2.

Equation of the line in slope-intercept formula,

Putting x₁ = 0, y₁ = 75000, we get

3.

Putting x = 10, we can compute the value of y to get the salary after 10 years.

∴ Tom's salary in ten years will be $95,000

when x=0.

when x=4.

1.Rate of change=

2. Slope intercept form of salary and number of years

   →[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

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.