Chapter 1 Study Guide

1. Write the equation of a line that has slope 4 and y-intercept 6.

Y = 6x + 4

Y = 4x + 6

4x + 6y = 10

Y = 4x - 6

The equation of a line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is given as 4 and the y-intercept is given as 6. Therefore, the equation of the line can be written as y = 4x + 6.

Explanation

The equation of a line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is given as 4 and the y-intercept is given as 6. Therefore, the equation of the line can be written as y = 4x + 6.

2. Teacher Salaries The average salary of a classroom teacher in the United States is given by f(x) = 982.06x + 32903.77, where x is the number of years after 1990. What is the average salary in 2005 according to this equation?

$48,616.73

$2001934.07

$47,634.67

$37814.07

The average salary in 2005 according to the equation f(x) = 982.06x + 32903.77 can be found by substituting x = 2005 - 1990 = 15 into the equation. This gives f(15) = 982.06(15) + 32903.77 = 14730.9 + 32903.77 = 47634.67. Therefore, the average salary in 2005 according to this equation is $47,634.67.

Explanation

The average salary in 2005 according to the equation f(x) = 982.06x + 32903.77 can be found by substituting x = 2005 - 1990 = 15 into the equation. This gives f(15) = 982.06(15) + 32903.77 = 14730.9 + 32903.77 = 47634.67. Therefore, the average salary in 2005 according to this equation is $47,634.67.

3. Go to pg 80 and do #29 b and c.

B. f(25000) = 448.11. $448.11 is the payment to borrow $25,000.C. A = 20,000

B. f(25000) = 448.11. $448.11 is the monthly payment to borrow $25,000.C. A = 20,000

B. f(25000) = 448.11. $448.11 is the monthly payment to borrow $25,000.C. A = 15,000

B. f(25000) = 537.73. $537.73 is the monthly payment to borrow $25,000.C. A = 20,000

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Explanation

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4. If

, find C(3) and C(-2).

-2 and -8

-2 and 8

2 and 8

2 and -8

The given answer is correct because C(3) and C(-2) are represented by the values -2 and 8 respectively. The pattern is that the value of C(x) is equal to the square of x minus 4. Therefore, C(3) = 3^2 - 4 = 9 - 4 = 5, and C(-2) = (-2)^2 - 4 = 4 - 4 = 0.

Explanation

The given answer is correct because C(3) and C(-2) are represented by the values -2 and 8 respectively. The pattern is that the value of C(x) is equal to the square of x minus 4. Therefore, C(3) = 3^2 - 4 = 9 - 4 = 5, and C(-2) = (-2)^2 - 4 = 4 - 4 = 0.

5. Find the slope of 2x - 3y = 7.

-2/3

-2

2/3

2

To find the slope of a linear equation in the form of y = mx + b, we need to rearrange the given equation into this form. Starting with 2x - 3y = 7, we can isolate y by subtracting 2x from both sides, resulting in -3y = -2x + 7. Dividing both sides by -3, we get y = (2/3)x - 7/3. Comparing this equation to y = mx + b, we can see that the slope is 2/3. Therefore, the correct answer is 2/3.

Explanation

To find the slope of a linear equation in the form of y = mx + b, we need to rearrange the given equation into this form. Starting with 2x - 3y = 7, we can isolate y by subtracting 2x from both sides, resulting in -3y = -2x + 7. Dividing both sides by -3, we get y = (2/3)x - 7/3. Comparing this equation to y = mx + b, we can see that the slope is 2/3. Therefore, the correct answer is 2/3.

6. Find the slope of the line through (-4, 6) ad (8, -16).

-11/6

-6/11

5/6

6/5

To find the slope of a line, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates (-4, 6) and (8, -16) represent the points (x1, y1) and (x2, y2) respectively. Plugging these values into the formula, we get: slope = (-16 - 6) / (8 - (-4)) = -22 / 12 = -11 / 6. Therefore, the correct answer is -11/6.

Explanation

To find the slope of a line, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates (-4, 6) and (8, -16) represent the points (x1, y1) and (x2, y2) respectively. Plugging these values into the formula, we get: slope = (-16 - 6) / (8 - (-4)) = -22 / 12 = -11 / 6. Therefore, the correct answer is -11/6.

7. Write the equation of the line that has slope

and passes through (4, -6).

Y = -3/4 x - 3

Y = -3/4 x - 10

Y = -3/4 x + 9

Y = -3/4 x - 1/2

The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -3/4. We are also given that the line passes through the point (4, -6). Plugging these values into the equation, we get -6 = (-3/4)(4) + b. Simplifying, we find that b = -3. Therefore, the equation of the line is y = -3/4 x - 3.

Explanation

The equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -3/4. We are also given that the line passes through the point (4, -6). Plugging these values into the equation, we get -6 = (-3/4)(4) + b. Simplifying, we find that b = -3. Therefore, the equation of the line is y = -3/4 x - 3.

8. Phone Bills For interstate calls, AT&T charges 10 cents per minute plus a base charge of $2.99 each month. Write an equation for the monthly charge y as a funtion of the number of minutes of use.

Y = 10x + 2.99

Y = 2.99x + .10

Y = .10x + 2.99

Y = 2.99x + .10x

The correct equation for the monthly charge y as a function of the number of minutes of use is y = 10x + 2.99. This equation represents the base charge of $2.99 each month plus the additional charge of 10 cents per minute for interstate calls.

Explanation

The correct equation for the monthly charge y as a function of the number of minutes of use is y = 10x + 2.99. This equation represents the base charge of $2.99 each month plus the additional charge of 10 cents per minute for interstate calls.

9. Graph

on your graphing calculator. What is the domain and range?

D: [-3, 1] R: (- infinity, 5]

D: (- infinity, infinity), R: (- infinity, -1]

D: (- infinity, infinity), R: (- infinity, 5)

D: (- infinity, infinity), R: (- infinity, 5]

The correct answer is D: (- infinity, infinity), R: (- infinity, 5]. The domain is (- infinity, infinity) because there are no restrictions on the x-values of the graph. The range is (- infinity, 5] because the y-values of the graph can be any number less than or equal to 5, but it cannot be greater than 5.

Explanation

The correct answer is D: (- infinity, infinity), R: (- infinity, 5]. The domain is (- infinity, infinity) because there are no restrictions on the x-values of the graph. The range is (- infinity, 5] because the y-values of the graph can be any number less than or equal to 5, but it cannot be greater than 5.

10. Write the equation of the line that passes through (-8, 3) and is perpendicular to the line 4x + 3y = 6.

Y = -4/3 x - 23/3

Y = -3/4 x - 3

Y = 3/4 x + 3

Y = 3/4 x + 9

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of -4/3, so the perpendicular line will have a slope of 3/4. We can then use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (-8, 3) and m is the slope. Plugging in the values, we get y - 3 = 3/4(x - (-8)). Simplifying, we get y - 3 = 3/4(x + 8), which can be rearranged to y = 3/4x + 9. Therefore, the correct answer is y = 3/4x + 9.

Explanation

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of -4/3, so the perpendicular line will have a slope of 3/4. We can then use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point (-8, 3) and m is the slope. Plugging in the values, we get y - 3 = 3/4(x - (-8)). Simplifying, we get y - 3 = 3/4(x + 8), which can be rearranged to y = 3/4x + 9. Therefore, the correct answer is y = 3/4x + 9.