Question
1,30
5,55
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=x+1
y is equal to x plus 1
y=x+25
y is equal to x plus 25
y=5x
y is equal to 5 x
y=5x+25
y is equal to 5 x plus 25
5,55
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=x+1
y is equal to x plus 1
y=x+25
y is equal to x plus 25
y=5x
y is equal to 5 x
y=5x+25
y is equal to 5 x plus 25
Answers
Answered by
GPT-4o mini
To find the equation of the trend line using the points (1, 30) and (5, 55), we first need to calculate the slope (m) of the line:
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{55 - 30}{5 - 1} = \frac{25}{4} = 6.25
\]
2. **Using the slope and one of the points to find the y-intercept (b)**. We'll use the point (1, 30):
The slope-intercept form of a line is \( y = mx + b \).
Substituting in the slope and the coordinates of the point:
\[
30 = 6.25(1) + b
\]
\[
30 = 6.25 + b
\]
To find \( b \):
\[
b = 30 - 6.25 = 23.75
\]
3. **Write the equation**:
Now, substituting \( m \) and \( b \) back into the slope-intercept form:
\[
y = 6.25x + 23.75
\]
This equation does not match any of the provided options directly. Let's rewrite the equation to see it in a similar format, but based on the options given, we can see that none of them exactly match.
However, if we simplify or modify this trend based on the closest match available:
- The option \( y = 5x + 25 \) is not quite accurate either, but if looking for a rough comparable measure or a misstep in slope where values simplify for textbook cases, we consider slope approximations.
Ultimately, based on the calculations, the correct equation is close to \( y = 6.25x + 23.75 \) and does not match any provided options perfectly. If you must choose from the given options, it seems they do not accurately represent the linear regression of the points given. The actual math shows the slope to be 6.25 (not aligning with any provided choices).
1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{55 - 30}{5 - 1} = \frac{25}{4} = 6.25
\]
2. **Using the slope and one of the points to find the y-intercept (b)**. We'll use the point (1, 30):
The slope-intercept form of a line is \( y = mx + b \).
Substituting in the slope and the coordinates of the point:
\[
30 = 6.25(1) + b
\]
\[
30 = 6.25 + b
\]
To find \( b \):
\[
b = 30 - 6.25 = 23.75
\]
3. **Write the equation**:
Now, substituting \( m \) and \( b \) back into the slope-intercept form:
\[
y = 6.25x + 23.75
\]
This equation does not match any of the provided options directly. Let's rewrite the equation to see it in a similar format, but based on the options given, we can see that none of them exactly match.
However, if we simplify or modify this trend based on the closest match available:
- The option \( y = 5x + 25 \) is not quite accurate either, but if looking for a rough comparable measure or a misstep in slope where values simplify for textbook cases, we consider slope approximations.
Ultimately, based on the calculations, the correct equation is close to \( y = 6.25x + 23.75 \) and does not match any provided options perfectly. If you must choose from the given options, it seems they do not accurately represent the linear regression of the points given. The actual math shows the slope to be 6.25 (not aligning with any provided choices).