The table represents some points on the graph of a linear function. Write a function that represents this relationship.
#5.
How to find the linear equation in your calculator:
1. Click on the + in your calculator to get a table. 2. Enter the points in the table. 3.Belowthetable,typein y1~mx1+b.
4. The m is your slope and the b is your y-intercept.
5. Type your equation in the box in slope-intercept form (
y=mx+b).
x
y
−4
10
−2
7
6
−5
y=
To find the linear equation, we first need to find the slope (m) using the formula:
m = (change in y) / (change in x)
m = (10 - 7) / (-4 - (-2))
m = 3 / -2
m = -1.5
Next, we need to find the y-intercept (b) by substituting one of the points into the equation y = mx + b. We can use the point (2, 7):
7 = (-1.5)(-2) + b
7 = 3 + b
b = 4
Therefore, the linear function representing the relationship is:
y = -1.5x + 4
The table represents some points on the graph of a linear function. Write a function that represents this relationship.
#6.
How to find the linear equation in your calculator:
1. Click on the + in your calculator to get a table. 2. Enter the points in the table. 3.Belowthetable,typein y1~mx1+b.
4. The m is your slope and the b is your y-intercept.
5. Type your equation in the box in slope-intercept form (
y=mx+b).
x
y
−7.5
12
−3.5
0
−1
−7.5
2
−16.5
3.5
−21
y=
To find the linear equation representing the relationship between the points, let's first calculate the slope (m) using the formula:
m = (change in y) / (change in x)
We can choose any two points to calculate the slope. Let's use the points (-7.5, 12) and (-3.5, 0):
m = (0 - 12) / (-3.5 - (-7.5))
m = -12 / 4
m = -3
Next, use the slope (m) to find the y-intercept (b) by substituting one of the points into the equation y = mx + b. Let's use the point (-1, -7.5):
-7.5 = -3(-1) + b
-7.5 = 3 + b
b = -10.5
Therefore, the linear function representing the relationship is:
y = -3x - 10.5
The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
#7.
Based on the table, which function models this situation?
f n =−3n+24 f n =−13n+16 f n =−3n+64 f n =−13n+8
To determine which function models the situation based on the table, we need to identify the correct relationship between the number of meals dispensed (n) and the amount of pet food remaining (f).
Looking at the table, we can see that the amount of pet food decreases with each meal dispensed. So, the coefficient in front of n should be negative for a correct model.
Let's evaluate each option using the information from the table:
1. f(n) = -3n + 24:
If we substitute n = 0 into this function, we get f(0) = -3(0) + 24 = 24. This fits the table.
2. f(n) = -13n + 16:
If we substitute n = 0 into this function, we get f(0) = -13(0) + 16 = 16. This does not fit the table.
3. f(n) = -3n + 64:
If we substitute n = 0 into this function, we get f(0) = -3(0) + 64 = 64. This does not fit the table.
4. f(n) = -13n + 8:
If we substitute n = 0 into this function, we get f(0) = -13(0) + 8 = 8. This does not fit the table.
Therefore, the function that best models this situation based on the table is:
f(n) = -3n + 24
Thetablerepresentssomepointsonthegraphoflinearfunction
f.
#8. Whichfunctionrepresents f?
f x =26 x−2
f x =−26 2x−1 f x =13 x−2
f x =−2 26x−1
To determine which function represents f based on the table, we need to find the function that matches the relationship between the given points.
Given the table:
x f(x)
2 24
6 52
Now, let's evaluate each option:
1. f(x) = 26x - 2:
f(2) = 26(2) - 2 = 52 - 2 = 50 (does not match)
f(6) = 26(6) - 2 = 156 - 2 = 154 (does not match)
2. f(x) = -26/2x - 1:
f(2) = -26/(2*2) - 1 = -26/4 - 1 = -6.5 - 1 = -7.5 (does not match)
f(6) = -26/(2*6) - 1 = -26/12 - 1 = -2.17 - 1 = -3.17 (does not match)
3. f(x) = 13(x - 2):
f(2) = 13(2 - 2) = 13(0) = 0 (does not match)
f(6) = 13(6 - 2) = 13(4) = 52 (matches)
4. f(x) = -2/26x - 1:
f(2) = -2/(26*2) - 1 = -2/52 - 1 = -0.038 - 1 = -1.038 (does not match)
f(6) = -2/(26*6) - 1 = -2/156 - 1 = -0.0128 - 1 = -1.0128 (does not match)
Therefore, the function that represents f based on the table is: f(x) = 13(x - 2)