Question
Which linear function has the steepest slope?
On a coordinate plane, a line goes through points (0, 1) and (1, negative 2).
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries 10, 13, 16, 19.
On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.
On a coordinate plane, a line goes through points (0, 1) and (1, negative 2).
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries 10, 13, 16, 19.
On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries 2, 4, 6, 8. Column 2 is labeled y with entries negative 4, negative 12, negative 20, negative 28.
Answers
GPT-4o mini
To determine which linear function has the steepest slope, we need to calculate the slope of each line provided.
1. **For the first line that goes through points (0, 1) and (1, -2)**:
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{1 - 0} = \frac{-3}{1} = -3
\]
2. **For the second line (the table with the points (3, 10), (6, 13), (9, 16), (12, 19))**:
From the table, we can find the slope using the first and last points (though you can use any two points). Let's choose (3, 10) and (12, 19):
\[
m = \frac{19 - 10}{12 - 3} = \frac{9}{9} = 1
\]
3. **For the third line that goes through points (0, -2) and (1, 0)**:
Again, using the slope formula:
\[
m = \frac{0 - (-2)}{1 - 0} = \frac{2}{1} = 2
\]
4. **For the fourth table (the points (2, -4), (4, -12), (6, -20), (8, -28))**:
Let's find the slope between the first and second points:
\[
m = \frac{-12 - (-4)}{4 - 2} = \frac{-12 + 4}{2} = \frac{-8}{2} = -4
\]
Now, we have the slopes for each line:
- First line: slope = -3
- Second line: slope = 1
- Third line: slope = 2
- Fourth line: slope = -4
To find the steepest slope, we compare the absolute values of these slopes:
- | -3 | = 3
- | 1 | = 1
- | 2 | = 2
- | -4 | = 4
The steepest slope is **-4** from the fourth line (which is steep in the negative direction, but steep regardless).
1. **For the first line that goes through points (0, 1) and (1, -2)**:
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{1 - 0} = \frac{-3}{1} = -3
\]
2. **For the second line (the table with the points (3, 10), (6, 13), (9, 16), (12, 19))**:
From the table, we can find the slope using the first and last points (though you can use any two points). Let's choose (3, 10) and (12, 19):
\[
m = \frac{19 - 10}{12 - 3} = \frac{9}{9} = 1
\]
3. **For the third line that goes through points (0, -2) and (1, 0)**:
Again, using the slope formula:
\[
m = \frac{0 - (-2)}{1 - 0} = \frac{2}{1} = 2
\]
4. **For the fourth table (the points (2, -4), (4, -12), (6, -20), (8, -28))**:
Let's find the slope between the first and second points:
\[
m = \frac{-12 - (-4)}{4 - 2} = \frac{-12 + 4}{2} = \frac{-8}{2} = -4
\]
Now, we have the slopes for each line:
- First line: slope = -3
- Second line: slope = 1
- Third line: slope = 2
- Fourth line: slope = -4
To find the steepest slope, we compare the absolute values of these slopes:
- | -3 | = 3
- | 1 | = 1
- | 2 | = 2
- | -4 | = 4
The steepest slope is **-4** from the fourth line (which is steep in the negative direction, but steep regardless).