Use the image to answer the question.
A scatterplot graph shows x-axis ranging from 0 to 100 and y-axis ranging from 0 to 50. Both axes are drawn in increments of 5 but labeled in increments of 10. Multiple points are plotted around a line that points upward to the right. The line passes approximately through left parenthesis 0 comma 30 right parenthesis, left parenthesis 15 comma 40 right parenthesis, left parenthesis 20 comma 45 right parenthesis, and left parenthesis 25 comma 47 right parenthesis. 14 points are plotted close to or on the line. The line has an arrowhead on the top of it.
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=34x
y equals Start Fraction 3 over 4 End Fraction x
y=−29x+30
y equals negative Start Fraction 2 over 9 End Fraction x plus 30
y=34x+30
y equals Start Fraction 3 over 4 End Fraction x plus 30
y=34x+45
y equals Start Fraction 3 over 4 End Fraction x plus 45
To find the equation of the trend line, we need to determine the slope and y-intercept.
The line passes through the points (0, 30), (15, 40), (20, 45), and (25, 47).
First, we can find the slope (m) using the formula:
m = (change in y) / (change in x)
Using the points (0, 30) and (25, 47), we have:
m = (47 - 30) / (25 - 0) = 17 / 25 = 0.68
Next, we can find the y-intercept (b) by substituting the slope and one of the points into the slope-intercept form equation (y = mx + b) and solving for b.
Using the point (0, 30), we have:
30 = 0.68 * 0 + b
30 = b
Therefore, the y-intercept is 30.
The equation of the trend line in slope-intercept form is:
y = 0.68x + 30
So, the correct answer is: y = 0.68x + 30.
y=34x+30
To determine the equation of the trend line, we need to calculate the slope and the y-intercept. Let's follow these steps:
1. Identify two points on the line.
From the scatterplot, two points that are approximately on the line are (0, 30) and (25, 47).
2. Calculate the slope.
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the values, we get: m = (47 - 30) / (25 - 0)
Simplifying: m = 17 / 25
3. Calculate the y-intercept.
The y-intercept (b) is the value of y when x is 0. From the scatterplot, we can see that the line intersects the y-axis at the point (0, 30), so b = 30.
4. Write the equation in slope-intercept form.
The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the values, we get: y = (17/25)x + 30.
Therefore, the equation in slope-intercept form of the trend line is y = (17/25)x + 30.