Which of the following is the equation of a line parallel to the line y = 4x + 1, passing through the point (5,1)?

Question

9. Which of the following is the equation of a line parallel to the line y = 4x + 1, passing through the point (5,1)?
4x + y = -19
4x - y = 19
-4x - y = 19
4x + y = 19

10. Which of the following is the equation of a line perpendicular to the line y = -10x + 1, passing through the point (5,7)?
1/10x-y=-13/12
1/10x+y=-13/2
1/10x+y=-13/2
-1/10x-y=13/2

12. How many solutions does the following system of equations have?

y-5/s+2
2y=5x+4
One
Two
Zero
Infinitely many

13. Assume f(x) = 2x + 8 and g(x) = 5. What is the value of (g o f)(3)?
5
70
18
15

15. Let h(x)=(g o f)(x)=x^2/x^2+1
Which of the following could be a possible decomposition of h(x)?
F(x)=x^2;g(x)=x/x+1
F(x)=x+1;g(x)=x^2
F(x)=x+1;g(x)=1/x^2
F(x)=x;g(x)=x/x+1

Answer 1

9) New line must have a slope m= 4 (since parallel) and pass thru the points (5,1)

 

     new line y = mx + b

                  y = 4x + b

                  1 = 4*5 + b

                  1 = 20 + b

                  b= -19

 

      new line is y = 4x - 19

      rearrange  4x - y = 19

 

10) New line must have a slope m = -1/(-10) = 1/10     (product of 2 slopes must = -1 since perpendicular)

 

      new line y = mx + b
                   y = 1/10x + b
                   7 = (1/10)*5 + b
                   7 = 1/2 + b
                   b= 13/2

     new line is y = 1/10x + 13/2
     rearrange 1/10x - y = -13/2    (Think first equation has a typo- should be 2 in denominator, not 12)

 

12) Cannot answer.  Must be a typo in first statement. An equation is a statement that the values of two mathematical expressions are equal (indicated by the sign =).

 

 

13) (g o f)(3)= g(f(x)).  But g(x) always equals 5.  So answer is 5.

 

15) h(x) = (g o f)(x)= g(f(x)).  If g(x) = x/(x + 1) and f(x) = x² , then g(f(x)) = x² /(x² + 1).  This is a possible solution.