Question
What are the slope and y-intercept of the line?
A scatterplot with about 20 points plotted in an upward trend along with a line of best fit that begins at the point zero comma 2 and passes through the point 4 comma 7 point 2.
The slope is approximately 3 and the y-intercept is 2.
The slope is approximately 1.33 and the y-intercept is 2.
The slope is approximately 2 and the y-intercept is 3.
The slope is approximately 2 and the y-intercept is 1.33.
A scatterplot with about 20 points plotted in an upward trend along with a line of best fit that begins at the point zero comma 2 and passes through the point 4 comma 7 point 2.
The slope is approximately 3 and the y-intercept is 2.
The slope is approximately 1.33 and the y-intercept is 2.
The slope is approximately 2 and the y-intercept is 3.
The slope is approximately 2 and the y-intercept is 1.33.
Answers
GPT-4o mini
To find the slope and y-intercept of the line, we can use the points given:
1. The y-intercept is the point where the line crosses the y-axis. According to the description, the line begins at the point (0, 2). Therefore, the y-intercept is 2.
2. To calculate the slope (\(m\)), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 2) and (4, 7.2):
- \(y_1 = 2\)
- \(y_2 = 7.2\)
- \(x_1 = 0\)
- \(x_2 = 4\)
Now, plug these values into the formula:
\[
m = \frac{7.2 - 2}{4 - 0} = \frac{5.2}{4} = 1.3
\]
Thus, the slope is approximately 1.3, which is close to 1.33.
So the answer is:
**The slope is approximately 1.33 and the y-intercept is 2.**
1. The y-intercept is the point where the line crosses the y-axis. According to the description, the line begins at the point (0, 2). Therefore, the y-intercept is 2.
2. To calculate the slope (\(m\)), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 2) and (4, 7.2):
- \(y_1 = 2\)
- \(y_2 = 7.2\)
- \(x_1 = 0\)
- \(x_2 = 4\)
Now, plug these values into the formula:
\[
m = \frac{7.2 - 2}{4 - 0} = \frac{5.2}{4} = 1.3
\]
Thus, the slope is approximately 1.3, which is close to 1.33.
So the answer is:
**The slope is approximately 1.33 and the y-intercept is 2.**