Use the image to answer the question.
An illustration of a scatterplot graph shows x-axis ranging from 0 to 15 in increments of 1 and y-axis ranging from 0 to 75 in increments of 5. Multiple points are plotted and a line points upward to the right with an arrowhead on the top.
The line passes approximately through left parenthesis 0 comma 25 right parenthesis, left parenthesis 1 comma 30 right parenthesis, left parenthesis 2 comma 35 right parenthesis, left parenthesis 7 comma 60 right parenthesis, and left parenthesis 10 comma 75 right parenthesis. 5 points are plotted to the line.
Write an equation in slope-intercept form of the trend line.
(1 point)
y= __
The equation in slope-intercept form of the trend line can be written as:
y = 5x + 25
To find the equation of the trend line, we need to determine the slope and y-intercept.
From the information given in the scatterplot, we can see that the line passes through the points (0, 25), (1, 30), (2, 35), (7, 60), and (10, 75).
We can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using points (0, 25) and (10, 75):
m = (75 - 25) / (10 - 0) = 50 / 10 = 5
Now that we have the slope (m), we can find the y-intercept (b) using the formula:
b = y - mx
Let's use the point (0, 25):
25 = 5(0) + b
25 = b
So the y-intercept (b) is 25.
Now we can write the equation of the trend line in slope-intercept form, which is:
y = mx + b
Substituting the values we calculated, we get:
y = 5x + 25
Therefore, the equation in slope-intercept form of the trend line is:
y = 5x + 25
To find the equation of the trend line, we need to determine the slope and the y-intercept.
First, we can calculate the slope using two points on the line: (0, 25) and (10, 75).
The slope formula is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates into the formula, we have:
slope = (75 - 25) / (10 - 0) = 50 / 10 = 5
Next, we can determine the y-intercept. Since the line passes through the point (0, 25), we know that the y-intercept is 25.
Now that we have the slope (5) and the y-intercept (25), we can write the equation of the trend line in slope-intercept form, y = mx + b:
y = 5x + 25
Therefore, the equation of the trend line is:
y = 5x + 25.