Use the image to answer the question.
An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 50 in increments of 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 45 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 4.5 comma 0 right parenthesis. 13 points are plotted close to the line.
Write an equation in slope-intercept form of the trend line.
(1 point)
y=__
y = -10x + 45
To find the equation of the trend line in slope-intercept form, we need to determine the slope and y-intercept.
From the given information, we can see that the trend line points downward to the right, indicating a negative slope.
To find the slope, we can choose any two points on the line and use the formula:
slope = (change in y-coordinates)/(change in x-coordinates)
Let's select the points (0, 45) and (4.5, 0):
slope = (0 - 45)/(4.5 - 0) = -45/4.5 = -10.
Now that we have the slope, we can use the equation y = mx + b and substitute the slope (-10) into the equation:
y = -10x + b.
To find the y-intercept (b), we can choose any point on the line and substitute its x and y coordinates into the equation.
Let's use the point (0, 45):
45 = -10(0) + b
45 = b.
Therefore, the equation of the trend line in slope-intercept form is:
y = -10x + 45.
To find the equation of the trend line, we need to determine the slope and y-intercept.
From the given information, we can observe that the trend line passes through the points (0, 45), (2, 25), (3, 15), and (4.5, 0).
1. Calculate the slope:
The slope (m) can be found by using the formula:
m = (change in y)/(change in x) = (y₂ - y₁)/(x₂ - x₁)
Taking the first two points (0, 45) and (2, 25):
m = (25 - 45)/(2 - 0) = -20/2 = -10
So, the slope (m) is -10.
2. Calculate the y-intercept (b):
The y-intercept is the value of y when x is equal to 0.
From the given information, we know that the line passes through the point (0, 45).
So, the y-intercept (b) is 45.
3. Write the equation in slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the calculated values, the equation is:
y = -10x + 45
Therefore, the equation in slope-intercept form of the trend line is:
y = -10x + 45.