Question
Which of the following graphed lines is parallel to y=34x+3
?(1 point)
Responses
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma 6 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 6 comma negative 4 right parenthesis and left parenthesis 4 comma 8 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma negative 1 right parenthesis and left parenthesis 4 comma 5 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma 8 right parenthesis and left parenthesis 8 comma negative 1 right parenthesis.
?(1 point)
Responses
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma 6 right parenthesis and left parenthesis 4 comma 0 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 6 comma negative 4 right parenthesis and left parenthesis 4 comma 8 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma negative 1 right parenthesis and left parenthesis 4 comma 5 right parenthesis.
A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Alt text will be read with the long description. A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1. The line is solid and passes through coordinates left parenthesis negative 4 comma 8 right parenthesis and left parenthesis 8 comma negative 1 right parenthesis.
Answers
GPT-4o mini
To determine which line is parallel to the line represented by the equation \( y = 34x + 3 \), we need to look at the slope of the line, which is \( 34 \). For two lines to be parallel, they must have the same slope.
We can calculate the slope of each of the mentioned lines by using the formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
1. **First line through \((-4, 6)\) and \( (4, 0)\)**:
\[
\text{slope} = \frac{0 - 6}{4 - (-4)} = \frac{-6}{8} = -\frac{3}{4}
\]
2. **Second line through \((-6, -4)\) and \( (4, 8)\)**:
\[
\text{slope} = \frac{8 - (-4)}{4 - (-6)} = \frac{8 + 4}{4 + 6} = \frac{12}{10} = \frac{6}{5}
\]
3. **Third line through \((-4, -1)\) and \( (4, 5)\)**:
\[
\text{slope} = \frac{5 - (-1)}{4 - (-4)} = \frac{5 + 1}{4 + 4} = \frac{6}{8} = \frac{3}{4}
\]
4. **Fourth line through \((-4, 8)\) and \( (8, -1)\)**:
\[
\text{slope} = \frac{-1 - 8}{8 - (-4)} = \frac{-9}{8 + 4} = \frac{-9}{12} = -\frac{3}{4}
\]
Now, we compare the calculated slopes with \( 34 \) (the slope of the given line):
- First line slope: \( -\frac{3}{4} \)
- Second line slope: \( \frac{6}{5} \)
- Third line slope: \( \frac{3}{4} \)
- Fourth line slope: \( -\frac{3}{4} \)
None of the lines have a slope equal to \( 34 \), which means that none of the provided lines are parallel to the line \( y = 34x + 3 \).
If you intended to find a line with a specific slope, please check if there may be any additional lines or information to consider!
We can calculate the slope of each of the mentioned lines by using the formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
1. **First line through \((-4, 6)\) and \( (4, 0)\)**:
\[
\text{slope} = \frac{0 - 6}{4 - (-4)} = \frac{-6}{8} = -\frac{3}{4}
\]
2. **Second line through \((-6, -4)\) and \( (4, 8)\)**:
\[
\text{slope} = \frac{8 - (-4)}{4 - (-6)} = \frac{8 + 4}{4 + 6} = \frac{12}{10} = \frac{6}{5}
\]
3. **Third line through \((-4, -1)\) and \( (4, 5)\)**:
\[
\text{slope} = \frac{5 - (-1)}{4 - (-4)} = \frac{5 + 1}{4 + 4} = \frac{6}{8} = \frac{3}{4}
\]
4. **Fourth line through \((-4, 8)\) and \( (8, -1)\)**:
\[
\text{slope} = \frac{-1 - 8}{8 - (-4)} = \frac{-9}{8 + 4} = \frac{-9}{12} = -\frac{3}{4}
\]
Now, we compare the calculated slopes with \( 34 \) (the slope of the given line):
- First line slope: \( -\frac{3}{4} \)
- Second line slope: \( \frac{6}{5} \)
- Third line slope: \( \frac{3}{4} \)
- Fourth line slope: \( -\frac{3}{4} \)
None of the lines have a slope equal to \( 34 \), which means that none of the provided lines are parallel to the line \( y = 34x + 3 \).
If you intended to find a line with a specific slope, please check if there may be any additional lines or information to consider!