10. Write an equation in point-slope form for the line through the given point with the given slope.
(5, 2); m=3
a. y+2=3(x-5) ***
b. y+2=3x-5
c. y-2=3(x+5)
d.y-2=3(x-5)
11. Write an equation in point-slope form for the line through the given point with the given slope.
(-10,-6); m=-5/8
a. y-6=-5/8(x-10)
b. y-6=-5/8(x+10)
c. y+6=-5/8(x+10) ***
d. y+10=-5/8(x+6)
14. Write y=(-3/4) in standard form using integers
a. 3x+4y=12
b. 3x+4y=-12
c. 3x-4y=12
d. -3x+4y=12 ***
24. You use a line of best fit for a set of data to make a prediction about an unknown value. The value correlation coefficient for your data set is -0.015. How confident can you be that your predicted value will be reasonably close to the actual value?
25. A college football coach wants to know if there is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. He sets up the following and records the data.
Every day for a week: counts how many times each player leg press 350 lbs
following week: 40 yd sprint each day
Table shows average number of leg-press & yard dash time for 7 players
What is the equation of best fit?
How many seconds should be expect a player to take to run 40 yards if that player can do 22 leg-press repetitions? Round any values to the nearest tenth, if necessary.
Leg Press (reps) 15 - 18 - 8 - 30 - 26 - 12 - 21
40-yard Dash (s) 5.2 - 6.3 - 6.8 - 8.2 - 8.0 - 5.3 - 5.9
#10 wrong -- see #11
#11 right
#14 has a typo, but I'm pretty sure you're wrong.
#24 what does a tiny correlation coefficient mean?
#25 use your favorite best-fit line tool. Many online.
@steve im not sure
10. To write an equation in point-slope form for the line through the given point (5, 2) with the slope of 3, you can use the point-slope form equation:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope.
Substituting the values into the equation, you get:
y - 2 = 3(x - 5)
So, the correct option is a. y+2=3(x-5).
11. Similarly, to write an equation in point-slope form for the line through the given point (-10, -6) with the slope of -5/8, you can use the point-slope form equation:
y - y1 = m(x - x1)
Substituting the values into the equation, you get:
y + 6 = (-5/8)(x + 10)
So, the correct option is c. y+6=-5/8(x+10).
14. To write y = -3/4 in standard form using integers, you need to eliminate the fraction.
Multiply the equation by 4 to get rid of the fraction:
4y = -3x
Now, move all the terms to the left side to get the equation in standard form:
3x + 4y = 0
Since the last option (-3x + 4y = 12) is not equivalent to the given equation, the correct option is d. -3x + 4y = 0.
24. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. The value of -0.015 indicates a very weak negative correlation. This means that there is almost no relationship between the variables, and therefore, you cannot be confident that your predicted value will be reasonably close to the actual value.
25. To find the equation of the best fit line, you can use linear regression to determine the line that best represents the relationship between leg presses and 40-yard dash times.
Using the given data, the equation of the best fit line can be calculated as:
y = mx + b,
where y represents the 40-yard dash time, x represents the leg press repetitions, m represents the slope of the line, and b represents the y-intercept.
By performing linear regression analysis on the given data, you can determine the values of m and b that minimize the sum of the squared differences between the observed 40-yard dash times and the predicted values based on the leg press repetitions.
Once you have the equation of the best fit line, you can substitute the value of x (22 leg-press repetitions) to find the expected 40-yard dash time.
Without the specific values of the leg press repetitions and 40-yard dash times in the given table, it is not possible to determine the equation of the best fit line or calculate the expected 40-yard dash time for a player with 22 leg-press repetitions.