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QuestionFind functions for average yearly earnings based on these points: Men (0,21), (30,66) and Women (0,20), (30,45).
(a) Determine M(x)=mx+bM(x)=m x+b for men.
(b) Determine W(x)=mx+bW(x)=m x+b for women.

Studdy Solution

STEP 1

Assumptions1. The points on the graph for men are (0,21) and (30,66), and for women are (0,20) and (30,45). . The x-values represent years after age21 and the y-values represent average yearly earnings.
3. We are to find linear functions in the form M(x)=mx+bM(x)=m x+b and W(x)=mx+bW(x)=m x+b that model the average yearly earnings for men and women respectively.

STEP 2

To find the function for men, we first need to calculate the slope (m) of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Plug in the given values for the points (0,21) and (30,66) into the slope formula.
m=66−2130−0m = \frac{66 -21}{30 -0}

STEP 4

Calculate the slope.
m=66−2130−0=4530=1.m = \frac{66 -21}{30 -0} = \frac{45}{30} =1.

STEP 5

Now that we have the slope, we can find the y-intercept (b) of the line. Since the line passes through the point (0,21), the y-intercept is21.
b=21b =21

STEP 6

Now we can write the function for men. Substitute the slope and y-intercept into the function form M(x)=mx+bM(x)=m x+b.
M(x)=1.5x+21M(x) =1.5x +21

STEP 7

To find the function for women, we first need to calculate the slope (m) of the line. Use the same slope formula as before.
m=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 8

Plug in the given values for the points (0,20) and (30,45) into the slope formula.
m=45−2030−0m = \frac{45 -20}{30 -0}

STEP 9

Calculate the slope.
m=45−2030−=2530=.8333m = \frac{45 -20}{30 -} = \frac{25}{30} =.8333

STEP 10

Now that we have the slope, we can find the y-intercept (b) of the line. Since the line passes through the point (0,20), the y-intercept is20.
b=20b =20

STEP 11

Now we can write the function for women. Substitute the slope and y-intercept into the function form W(x)=mx+bW(x)=m x+b.
W(x)=0.8333x+20W(x) =0.8333x +20The functions that model the average yearly earnings for men and women xx years after age21 are M(x)=.5x+21M(x) =.5x +21 and W(x)=0.8333x+20W(x) =0.8333x +20 respectively.

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