To create a table with these conditions, we need to find five points that satisfy the given conditions: the y-intercept is 5 and the slope is 3.
Considering the equation of a straight line, y = mx + b, where m is the slope and b is the y-intercept, we can plug in the given values to determine the corresponding y-values for various x-values.
Let's choose five different x-values and substitute them into the equation:
1) x = 0:
y = 3(0) + 5 = 0 + 5 = 5
2) x = 1:
y = 3(1) + 5 = 3 + 5 = 8
3) x = 2:
y = 3(2) + 5 = 6 + 5 = 11
4) x = -1:
y = 3(-1) + 5 = -3 + 5 = 2
5) x = -2:
y = 3(-2) + 5 = -6 + 5 = -1
Now, we have five points that satisfy both conditions:
(0, 5)
(1, 8)
(2, 11)
(-1, 2)
(-2, -1)
Thus, the table is as follows:
| x | y |
|-------|-------|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| -1 | 2 |
| -2 | -1 |
Create a table that has 5 points that meets both of the following conditions:
the y-intercept is 5
the slope is 3
11 answers
i dont get it
I apologize for any confusion. Let's break it down step by step.
To find a point that meets both conditions, we need to find an x-value and its corresponding y-value that satisfy the given conditions: y-intercept is 5 and slope is 3.
1) The y-intercept is the value of y when x = 0. Since the y-intercept is 5, we have one point: (0, 5).
2) The slope represents the change in y for every unit change in x. In this case, the slope is 3. This means that for every increase of 1 in x, y increases by 3.
Using this information, we can find four more points by changing the x-values and calculating the corresponding y-values:
- When x = 1, y = (slope * x) + y-intercept = (3 * 1) + 5 = 3 + 5 = 8. So, we have the point (1, 8).
- When x = 2, y = (3 * 2) + 5 = 6 + 5 = 11. So, we have the point (2, 11).
- When x = -1, y = (3 * -1) + 5 = -3 + 5 = 2. So, we have the point (-1, 2).
- When x = -2, y = (3 * -2) + 5 = -6 + 5 = -1. So, we have the point (-2, -1).
Thus, the table is as follows:
| x | y |
|-------|-------|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| -1 | 2 |
| -2 | -1 |
I hope this explanation clarifies it for you. Let me know if you have any further questions.
To find a point that meets both conditions, we need to find an x-value and its corresponding y-value that satisfy the given conditions: y-intercept is 5 and slope is 3.
1) The y-intercept is the value of y when x = 0. Since the y-intercept is 5, we have one point: (0, 5).
2) The slope represents the change in y for every unit change in x. In this case, the slope is 3. This means that for every increase of 1 in x, y increases by 3.
Using this information, we can find four more points by changing the x-values and calculating the corresponding y-values:
- When x = 1, y = (slope * x) + y-intercept = (3 * 1) + 5 = 3 + 5 = 8. So, we have the point (1, 8).
- When x = 2, y = (3 * 2) + 5 = 6 + 5 = 11. So, we have the point (2, 11).
- When x = -1, y = (3 * -1) + 5 = -3 + 5 = 2. So, we have the point (-1, 2).
- When x = -2, y = (3 * -2) + 5 = -6 + 5 = -1. So, we have the point (-2, -1).
Thus, the table is as follows:
| x | y |
|-------|-------|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| -1 | 2 |
| -2 | -1 |
I hope this explanation clarifies it for you. Let me know if you have any further questions.
dose (3,14) and (4,17) work to?
No, the points (3,14) and (4,17) do not satisfy the given conditions of the y-intercept being 5 and the slope being 3.
To verify this, let's calculate the slope between the points (3,14) and (4,17):
Slope = (Change in y)/(Change in x) = (17-14)/(4-3) = 3/1 = 3
The calculated slope of 3 matches the desired slope of 3. However, the y-intercept is not 5 for either of these points.
For the point (3,14), the y-intercept can be calculated using the slope-intercept form of a line (y = mx + b):
14 = 3(3) + b
14 = 9 + b
b = 14 - 9
b = 5
The y-intercept for the point (3,14) is indeed 5, so it satisfies that condition. However, the y-intercept is not 5 for the point (4,17).
Therefore, only the points (0,5), (1,8), (2,11), (-1,2), and (-2,-1) satisfy both conditions.
To verify this, let's calculate the slope between the points (3,14) and (4,17):
Slope = (Change in y)/(Change in x) = (17-14)/(4-3) = 3/1 = 3
The calculated slope of 3 matches the desired slope of 3. However, the y-intercept is not 5 for either of these points.
For the point (3,14), the y-intercept can be calculated using the slope-intercept form of a line (y = mx + b):
14 = 3(3) + b
14 = 9 + b
b = 14 - 9
b = 5
The y-intercept for the point (3,14) is indeed 5, so it satisfies that condition. However, the y-intercept is not 5 for the point (4,17).
Therefore, only the points (0,5), (1,8), (2,11), (-1,2), and (-2,-1) satisfy both conditions.
Create a table that has 5 points that meets both of the following conditions:
the y-intercept is 5
the slope is 3
Explain how you know that the y-intercept is 5.
Explain how you know that the slope is 3.
the y-intercept is 5
the slope is 3
Explain how you know that the y-intercept is 5.
Explain how you know that the slope is 3.
To create a table with five points that meet the given conditions (y-intercept of 5 and slope of 3), we can follow the steps below:
1. Determine the y-intercept:
The y-intercept is the value of y when x is 0. In this case, the given condition is that the y-intercept is 5, so we know that the point (0, 5) must be included in the table.
2. Determine the slope:
The slope represents the rate at which y changes with each unit change in x. In this case, the given condition is that the slope is 3, which means that for every increase of 1 in x, y should increase by 3 units. This gives us the relationship: Δy/Δx = 3.
3. Choose four additional x-values:
To find the corresponding y-values, we can select four different x-values and use the slope to determine the change in y. For simplicity, let's choose x = 1, x = 2, x = -1, and x = -2.
4. Calculate the corresponding y-values:
By plugging the chosen x-values into the equation y = mx + b, where m represents the slope and b is the y-intercept, we can calculate the values of y.
Let's create the table based on these steps:
| x | y |
|-----|-----|
| 0 | 5 |
| 1 | 3(1) + 5 = 3 + 5 = 8 |
| 2 | 3(2) + 5 = 6 + 5 = 11 |
| -1 | 3(-1) + 5 = -3 + 5 = 2 |
| -2 | 3(-2) + 5 = -6 + 5 = -1 |
Explanation:
Knowing that the y-intercept is 5:
We are given the condition that the y-intercept is 5. The y-intercept represents the value of y when x = 0. By setting x = 0 in the equation y = mx + b and solving for y, we find that y = 5. The point (0, 5) satisfies this condition.
Knowing that the slope is 3:
The slope represents the change in y over the change in x, or the "rise over run." In this case, the slope is given to be 3. It means that for every increase of 1 in x, y will increase by 3 units. This can be seen as the coefficient of x in the equation y = mx + b. Therefore, we know that the slope is 3.
1. Determine the y-intercept:
The y-intercept is the value of y when x is 0. In this case, the given condition is that the y-intercept is 5, so we know that the point (0, 5) must be included in the table.
2. Determine the slope:
The slope represents the rate at which y changes with each unit change in x. In this case, the given condition is that the slope is 3, which means that for every increase of 1 in x, y should increase by 3 units. This gives us the relationship: Δy/Δx = 3.
3. Choose four additional x-values:
To find the corresponding y-values, we can select four different x-values and use the slope to determine the change in y. For simplicity, let's choose x = 1, x = 2, x = -1, and x = -2.
4. Calculate the corresponding y-values:
By plugging the chosen x-values into the equation y = mx + b, where m represents the slope and b is the y-intercept, we can calculate the values of y.
Let's create the table based on these steps:
| x | y |
|-----|-----|
| 0 | 5 |
| 1 | 3(1) + 5 = 3 + 5 = 8 |
| 2 | 3(2) + 5 = 6 + 5 = 11 |
| -1 | 3(-1) + 5 = -3 + 5 = 2 |
| -2 | 3(-2) + 5 = -6 + 5 = -1 |
Explanation:
Knowing that the y-intercept is 5:
We are given the condition that the y-intercept is 5. The y-intercept represents the value of y when x = 0. By setting x = 0 in the equation y = mx + b and solving for y, we find that y = 5. The point (0, 5) satisfies this condition.
Knowing that the slope is 3:
The slope represents the change in y over the change in x, or the "rise over run." In this case, the slope is given to be 3. It means that for every increase of 1 in x, y will increase by 3 units. This can be seen as the coefficient of x in the equation y = mx + b. Therefore, we know that the slope is 3.
would this work?
x | y
-------
-1 | 2
-2 | -1
0 | 5
1 | 8
2 | 11
x | y
-------
-1 | 2
-2 | -1
0 | 5
1 | 8
2 | 11
Yes, the table you have provided:
| x | y |
|-----|-----|
| -1 | 2 |
| -2 | -1 |
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
satisfies both conditions: the y-intercept is 5, and the slope is 3.
- The point (0, 5) shows that the line intersects the y-axis at y = 5, confirming the y-intercept of 5.
- The differences in y-coordinate between the points (-1, 2) and (0, 5) and between the points (0, 5) and (1, 8) are both 3, which corresponds to the slope of 3.
Hence, this table meets both conditions. Great job!
| x | y |
|-----|-----|
| -1 | 2 |
| -2 | -1 |
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
satisfies both conditions: the y-intercept is 5, and the slope is 3.
- The point (0, 5) shows that the line intersects the y-axis at y = 5, confirming the y-intercept of 5.
- The differences in y-coordinate between the points (-1, 2) and (0, 5) and between the points (0, 5) and (1, 8) are both 3, which corresponds to the slope of 3.
Hence, this table meets both conditions. Great job!
would this work?
x | y
-------
0 | 5
1 | 8
2 | 11
3 | 14
4 | 17
x | y
-------
0 | 5
1 | 8
2 | 11
3 | 14
4 | 17
No, the table you provided,
| x | y |
|-----|-----|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| 3 | 14 |
| 4 | 17 |
does not meet the condition of the given slope being 3.
To verify the slope, we can calculate the differences in y-coordinates divided by the differences in x-coordinates. Taking the difference between consecutive points, we get:
- For (0, 5) and (1, 8): (8 - 5) / (1 - 0) = 3 / 1 = 3, which matches the desired slope of 3.
- However, the differences between the other consecutive points do not match the slope of 3:
- For (1, 8) and (2, 11): (11 - 8) / (2 - 1) = 3 / 1 = 3, which is correct.
- For (2, 11) and (3, 14): (14 - 11) / (3 - 2) = 3 / 1 = 3, which is correct.
- For (3, 14) and (4, 17): (17 - 14) / (4 - 3) = 3 / 1 = 3, which is correct.
Therefore, the table you provided does meet the condition of the y-intercept being 5, but it does not meet the condition of the slope being 3.
| x | y |
|-----|-----|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| 3 | 14 |
| 4 | 17 |
does not meet the condition of the given slope being 3.
To verify the slope, we can calculate the differences in y-coordinates divided by the differences in x-coordinates. Taking the difference between consecutive points, we get:
- For (0, 5) and (1, 8): (8 - 5) / (1 - 0) = 3 / 1 = 3, which matches the desired slope of 3.
- However, the differences between the other consecutive points do not match the slope of 3:
- For (1, 8) and (2, 11): (11 - 8) / (2 - 1) = 3 / 1 = 3, which is correct.
- For (2, 11) and (3, 14): (14 - 11) / (3 - 2) = 3 / 1 = 3, which is correct.
- For (3, 14) and (4, 17): (17 - 14) / (4 - 3) = 3 / 1 = 3, which is correct.
Therefore, the table you provided does meet the condition of the y-intercept being 5, but it does not meet the condition of the slope being 3.
1 answer