Question

1. an elevator rises steadily up a skyscraper. after 4 s it is 33 m above the ground. two seconds later it is 47 m above the ground. which equation models its height, y, with respect to time, x? a y - 33=-7(x - 4) b y - 47=-7(x - 2) c y - 33 = 7(x - 4) d y + 33 = 7(x + 4) 9. what are the x - and y - intercepts of the graph of 5x + 8y = 20? graph the equation. x - intercept: y - intercept: 10. jake needs to buy 120 beverages for a party. write an equation, in standard form, that determines the numbers of 8 - packs of juice x and 12 - packs of water y that jake can buy? x + y = 11. for the situation in item 10, select all the ordered pairs that represent combinations of packs of juice and packs of water that jake can buy. a. (0, 10) b. (12, 2) c. (-2, 11) d. (7 1/2, 5) e. (30, -10) 12. graph the equation 4x + 8y = 16. what is the slope of the graph? slope: 13. what is the equation in slope - intercept form of the line that passes through the point (-0.5, 7) and is parallel to the graph of y=-8x - 2? y = x + 14. select all the equations that represent lines that are perpendicular to the graph of 6x + 18y = 5. a. y = 3x - 10 b. x = 3 c. y + 6 = 3(x - 15) d. 3x + 9y = 8 e. 2x - 3y = 5 15. overline ab of rectangle abcd passes through the point (2, 0) and is perpendicular to the graph of y = 1/4x - 3. overline cd is parallel to overline ab and passes through the point (-1, 6). select the equation in slope - intercept form of the line that includes overline cd. a y = 1/4x + 2 b y=-1/4x + 2 c y=-4x + 2 d y = 4x + 2

Explanation:

8.

Step1: Find the rate of change

The elevator is at 33 m after 4 s and 47 m after 6 s (4 + 2 s). The rate of change (slope) $m=\frac{47 - 33}{6 - 4}=\frac{14}{2}=7$ m/s.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(x_1,y_1)=(4,33)$ and $m = 7$, we get $y-33 = 7(x - 4)$.

Step1: Find x - intercept

Set $y = 0$ in the equation $5x+8y=20$. Then $5x=20$, so $x = 4$.

Step2: Find y - intercept

Set $x = 0$ in the equation $5x + 8y=20$. Then $8y=20$, so $y=\frac{20}{8}=\frac{5}{2}=2.5$.

Let $x$ be the number of 8 - packs of juice and $y$ be the number of 12 - packs of water. The total number of beverages is 120. So, $8x + 12y=120$.

Answer:

C

9.