write the equation in slope - intercept form. 1. contains the points (-4,12) and (12,-16) write the equation…

write the equation in slope - intercept form. 1. contains the points (-4,12) and (12,-16) write the equation of the line that is perpendicular to y=-2x + 4 and contains the point (2,24) numerically a physics student obtains the following data involving a ball rolling down an inclined plane, where t is the elapsed time in seconds and y is the distance traveled in inches. t 0 1 2 3 4 5 y 0 1.2 4.8 10.8 19.2 30 3. what is the average velocity of the ball for the indicated time interval? 4. which interval was the ball travelling fastest? 5. predict the distance at 6 seconds. justify your prediction. graphically the graph shows the minimum salaries in major league baseball over a recent 18 - year period and the average salaries in major league baseball over the same period. salaries are measured in dollars and time is measured after the starting year (year 0). 6. which line is which, and how do you know? 7. after peter ueberroths resignation as baseball commissioner in 1988 and his successors untimely death in 1989, the team owners broke free of previous restrictions and began an era of competitive spending on player salaries. identify where the 1990 salaries appear in the graph and explain how you can spot them. 8. the owners attempted to halt the uncontrolled spending by proposing a salary cap, which prompted a players strike in 1994. the strike caused the 1995 season to be shortened and left many fans angry. identify where the 1995 salaries appear in the graph and explain how you can spot them.

write the equation in slope - intercept form. 1. contains the points (-4,12) and (12,-16) write the equation of the line that is perpendicular to y=-2x + 4 and contains the point (2,24) numerically a physics student obtains the following data involving a ball rolling down an inclined plane, where t is the elapsed time in seconds and y is the distance traveled in inches. t 0 1 2 3 4 5 y 0 1.2 4.8 10.8 19.2 30 3. what is the average velocity of the ball for the indicated time interval? 4. which interval was the ball travelling fastest? 5. predict the distance at 6 seconds. justify your prediction. graphically the graph shows the minimum salaries in major league baseball over a recent 18 - year period and the average salaries in major league baseball over the same period. salaries are measured in dollars and time is measured after the starting year (year 0). 6. which line is which, and how do you know? 7. after peter ueberroths resignation as baseball commissioner in 1988 and his successors untimely death in 1989, the team owners broke free of previous restrictions and began an era of competitive spending on player salaries. identify where the 1990 salaries appear in the graph and explain how you can spot them. 8. the owners attempted to halt the uncontrolled spending by proposing a salary cap, which prompted a players strike in 1994. the strike caused the 1995 season to be shortened and left many fans angry. identify where the 1995 salaries appear in the graph and explain how you can spot them.

Answer

1.

Explanation:

Step1: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given points $(-4,12)$ and $(12,-16)$, we have $m=\frac{-16 - 12}{12-(-4)}=\frac{-28}{16}=-\frac{7}{4}$.

Step2: Use the point - slope form $y - y_1=m(x - x_1)$ and convert to slope - intercept form

Using the point $(-4,12)$ and $m =-\frac{7}{4}$, we have $y - 12=-\frac{7}{4}(x + 4)$. Expand: $y-12=-\frac{7}{4}x-7$. Add 12 to both sides: $y=-\frac{7}{4}x + 5$.

Answer:

$y =-\frac{7}{4}x + 5$

2.

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the line $y=-2x + 4$ is $m_1=-2$. The slope of a line perpendicular to it, $m_2$, satisfies $m_1m_2=-1$. So $-2m_2=-1$, then $m_2=\frac{1}{2}$.

Step2: Use the point - slope form and convert to slope - intercept form

Using the point $(2,24)$ and $m_2=\frac{1}{2}$, we have $y - 24=\frac{1}{2}(x - 2)$. Expand: $y-24=\frac{1}{2}x-1$. Add 24 to both sides: $y=\frac{1}{2}x + 23$.

Answer:

$y=\frac{1}{2}x + 23$

3.

Explanation:

Step1: Recall the average - velocity formula

The average - velocity formula is $v_{avg}=\frac{\Delta y}{\Delta t}=\frac{y_2 - y_1}{t_2 - t_1}$. Let's assume the time interval is not specified. If we consider the interval from $t = 0$ to $t = 5$, then $y_1 = 0$, $y_2=30$, $t_1 = 0$, $t_2 = 5$.

Step2: Calculate the average velocity

$v_{avg}=\frac{30 - 0}{5 - 0}=6$ inches per second.

Answer:

6 inches per second

4.

Explanation:

Step1: Calculate the average velocity for each interval

For the interval $[0,1]$: $v_1=\frac{1.2 - 0}{1 - 0}=1.2$ inches per second. For the interval $[1,2]$: $v_2=\frac{4.8 - 1.2}{2 - 1}=3.6$ inches per second. For the interval $[2,3]$: $v_3=\frac{10.8 - 4.8}{3 - 2}=6$ inches per second. For the interval $[3,4]$: $v_4=\frac{19.2 - 10.8}{4 - 3}=8.4$ inches per second. For the interval $[4,5]$: $v_5=\frac{30 - 19.2}{5 - 4}=10.8$ inches per second.

Step2: Compare the average velocities

We can see that the ball is traveling fastest in the interval $[4,5]$.

Answer:

The interval $[4,5]$

5.

Explanation:

Step1: Observe the pattern of the data

We notice that the distances $y$ seem to follow the quadratic relationship $y = 0.6t^{2}$ (since when $t = 1$, $y=0.6\times1^{2}=0.6$; when $t = 2$, $y=0.6\times2^{2}=2.4$; when $t = 3$, $y=0.6\times3^{2}=5.4$; when $t = 4$, $y=0.6\times4^{2}=9.6$; when $t = 5$, $y=0.6\times5^{2}=15$). In fact, the correct relationship is $y = 0.6t^{2}$.

Step2: Predict the distance at $t = 6$

When $t = 6$, $y=0.6\times6^{2}=21.6$ inches.

Answer:

21.6 inches

6 - 8 are not fully solvable without the actual graph details. But the general approach for 6:

We can look at the characteristics of the lines such as slope (steeper line has a larger absolute - value of slope), intercepts, and trends over time to identify which line represents the minimum salary and which represents the average salary. For 7 and 8, we would look for the points on the graph corresponding to the years 1990 and 1995 respectively, which might be identified by changes in the slope or level of the lines due to the described events (era of competitive spending and strike).