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valkas [14]
3 years ago
7

the slope of a graphed line is 5 and the y-intercept is (0,3/4), what is the slope-intercept equation of the line?

Mathematics
1 answer:
DIA [1.3K]3 years ago
7 0

ANSWER

A. \:  \: y = 5x +  \frac{3}{4}

EXPLANATION

The slope-intercept form of an equation is given by;

y = mx  + c

wherever m is the slope and c is y-value of the y-intercept.

It was given that the slope is 5.

This implies that,

m = 5

The y-intercept is

(0, \frac{3}{4})

This means that,

c =  \frac{3}{4}

We plug in the values to obtain,

y = 5x +  \frac{3}{4}

The correct choice is A.

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Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

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Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

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