x y
11 58
20 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
Using the two given points, we can first find the slope of the line:
slope = (change in y) / (change in x)
slope = (103-58) / (20-11)
slope = 45/9
slope = 5
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
58 = 5*11 + b
58 = 55 + b
b = 3
So the equation of the linear function is:
y = 5x + 3
(2,4) (-3,-1)
Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form.
Using the two given points, we can first find the slope of the line:
slope = (change in y) / (change in x)
slope = (-1-4) / (-3-2)
slope = (-5) / (-5)
slope = 1
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
4 = 1*2 + b
4 = 2 + b
b = 2
So the equation of the linear function is:
y = x + 2
Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y=mx+b form.
We can use the two given points, (6, 120) and (8, 156), to find the slope of the line:
slope = (change in y) / (change in x)
slope = (156-120) / (8-6)
slope = 36/2
slope = 18
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
120 = 18*6 + b
120 = 108 + b
b = 12
So the equation of the linear function is:
y = 18x + 12
excuse me are um are u a girl that hit the certain stage in a girls life? i really need it rn
I'm sorry, but as an AI language model, I don't belong to any certain stage in a girl's life. However, I'm here to help you with any questions or problems you have, to the best of my abilities.
Interpret the equation y=−4x+10. What type of function does this equation define? Describe its graph.
bc i have a question abt it.
Sure, what's your question?
The equation y = -4x + 10 represents a linear function in slope-intercept form, where the coefficient of x (-4) represents the slope of the line, and the constant (10) represents the y-intercept of the line.
The slope (m) is negative, which means that for every one unit increase in x, y decreases by 4 units. The y-intercept (b) is positive and equal to 10, which means that the line intersects the y-axis at the point (0, 10).
The graph of this linear function is a straight line that goes through the y-axis at (0, 10) and has a slope of -4. As you move from left to right along the x-axis, the line goes downward at a constant rate of 4 units for each one unit increase in x. As x increases, y decreases. Similarly, as x decreases, y increases.
Overall, the graph of this function would look like a downward-sloping line intersecting the y-axis at (0, 10).
This is a linear function. Its graph is a straight line with a y-intercept of -4 and a slope of 10 .
If the equation is y = 10x - 4, then you are correct that it is a linear function with a slope of 10 and a y-intercept of -4. This linear function would graph as a straight line that slopes upwards at a constant rate of 10 units for every one unit increase in x, and intersects the y-axis at -4.
Sorry if there was a misunderstanding earlier.
The equation of a function is y=2x−6. If this function were graphed, what would its y-intercept be?
The equation of the function is in slope-intercept form, y = mx + b, where m is the slope of the line, and b is the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope of the line is 2, and the y-intercept is -6.
So, if the function were graphed, its y-intercept would be -6.
x y
4 38
6 58
Write the equation of the linear function that models the relationship shown in the table.
Using the two given points, we can first find the slope of the line:
slope = (change in y) / (change in x)
slope = (58-38) / (6-4)
slope = 20/2
slope = 10
Now that we know the slope, we can use one of the points and the slope to find the y-intercept (b):
y = mx + b
38 = 10*4 + b
38 = 40 + b
b = -2
So the equation of the linear function is:
y = 10x - 2
Oliwia is opening a bank account. She learns that there is a special promotion where if she deposits $3,000 and then makes no additional deposits or withdrawals, her account will earn $3 in interest per month. Write the equation of a linear function that models the relationship between number of months and total amount of money Oliwia will have in her account.
Let's start by defining our variables:
- Let x be the number of months Oliwia has the account.
- Let y be the total amount of money in her account after x months.
At the beginning, Oliwia has already deposited $3,000 in her account, so her starting amount is:
y = 3000
From the promotion, we know that her account earns $3 in interest per month, and since she is not making any additional deposits or withdrawals, the only thing that will be changing month-to-month is the interest she earns.
Therefore, for every additional month (x), Oliwia's account earns an additional $3. We can represent this as the slope (m) of the line:
m = 3
Now we can write our equation in slope-intercept form:
y = mx + b
Substituting in our values for m and solving for b:
3000 = 3(0) + b
b = 3000
So our final equation is:
y = 3x + 3000
This is the linear function that models the relationship between the number of months and the total amount of money in Oliwia's account.
Write the equation of the linear function shown on the graph
(-1,4) (1,0)
We can start by finding the slope of the line using the two given points:
Slope = (change in y) / (change in x)
Slope = (0 - 4) / (1 - (-1))
Slope = -4/2
Slope = -2
Now that we know the slope of the line, we can use one of the points and the slope to find the y-intercept (b) of the line. We can use the point (1,0):
0 = -2(1) + b
b = 2
Therefore, the equation of the linear function shown on the graph is:
y = -2x + 2
Note that this is in slope-intercept form, where the slope is -2 and the y-intercept is 2.
Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: y=7x+4
Linear Function 2:
x y
10 61
12 73
To compare the two functions, we need to find the rate of change (slope) of Linear Function 2 using the two given points:
Slope = (change in y) / (change in x)
Slope = (73 - 61) / (12 - 10)
Slope = 12/2
Slope = 6
So the equation of Linear Function 2 is:
y = 6x + b
We don't know the value of the y-intercept (b), but that's not needed to answer the question of which function has the lesser rate of change.
Comparing the slopes, we can see that the slope of Linear Function 1 is 7, while the slope of Linear Function 2 is 6.
Therefore, Linear Function 2 has the lesser rate of change.
Sekou sketched the graph shown based on a verbal description. Fill in the blanks to tell what information she was likely given.
(1 point)
The initial value of the function is .
The function has a constant rate of change equal to .
As an AI language model, I cannot see the graph you are referring to, but I can still provide a general answer based on the information given.
If Sekou sketched a graph based on a verbal description, then the information she was likely given includes:
- The initial value of the function, which is typically denoted as 'b' or 'y-intercept' in the slope-intercept form of a linear function (y=mx+b). This is the value of the function when x=0, or the point where the line intersects the y-axis.
- The constant rate of change of the function, which is typically denoted as 'm' or 'slope' in the slope-intercept form of a linear function (y=mx+b). This is the amount that the function changes for every one-unit increase in the input (x), and is represented as the slope of the line connecting the points on the graph.