The attachment is a bit difficult to read, and long. I'll make some suggestions and add some detail to a few of the problems, but would ask that these suggestions be applied to other problems to find the answers.
Step-by-step explanation:
9. Coinciding lines line on top of each other. I.e., they are the same equation. If we take A, for example, we can reduce the second expression by dividing by 2: (2x+4y=6)/2 = (x + 2y = 3). This matches the first expression (x + 2y = 3). ! Whoa, that went fast.
10. (x+8)(x-8) = x² +8x -8x - 64 = x² - 64
11. I don't have the time to explain how one can factor, but practice is important. And I don't know if this is completely factored, but it matches one of the options. Try (n-2)(n²+2n + 4) [n³ +2n² +4n - 2n² -4n -8 = n³ - 8. It works.
12. The denominators are the same, so add the numerators and keep the denominator. (7x+4y)/x²y
13. The slope is the "Rise" over the "Run." (3,4), (8,-1) Rise = (-1 - 4) = -5. Run = (8-3) = 5 Slope = -(5/5) = -1
14. A line with a positive slope will move upwards as x increases. We can eliminate options C and D immediately. That leaves A and B. The line we are looking for is y = 5x + b. We are not given b, the y-intercept, so determine the slopes of both lines: I get 4 for A and 5 for B. To confirm B is correct, we could calculate b for y=5x+b by using given point, (2,3). 3 = 5*2 + b, b = -7. We can't see this point (0,-7) on the graph, but it appears correct. B is the best answer.
15. The line will have the form of y=mx+b. Calculate m, the slope, from the two points (3,1) and (4,7). Rise = 6, Run = 1 Slope = 6. y=6x+b. Find b by using either of the given poins and solving for b. I'll choose (3,1). y=6x+b; 1 = 18 + b; b = -17. The equation is y=6x-17. Rearrange option A (y =6x - 17).
16. The second value in each factor must, when multiplied together, equal the final term of the original expression, -9y². I see only one option for which that is true, C. Multiply the two factors in C to be certain, and you'll find they result in the correct expression.
