The image contains a scatter plot graph with a series of black dots representing data points plotted against a grid background. The x-axis is labeled “x” and ranges from 0 to 10, while the y-axis is labeled “y” and ranges from 0 to 50. A line of best fit, represented by an orange arrow, is drawn through the data points, showing a negative linear relationship between variables x and y. Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AWrite an equation in slope-intercept form of the trend line.
To write the equation of the trend line in slope-intercept form (y = mx + b), we need to determine the slope (m) and y-intercept (b) based on the graph.
From the graph, we can see that the trend line has a negative slope, as it is sloping downwards from left to right.
To calculate the slope:
First data point: (0, 50)
Second data point: (10, 0)
Slope (m) = (change in y) / (change in x)
m = (0 - 50) / (10 - 0)
m = -50 / 10
m = -5
Now that we have the slope (m), we can use one of the data points to find the y-intercept (b) by substituting it into the slope-intercept form equation.
Using the first data point (0, 50):
50 = -5(0) + b
b = 50
Therefore, the equation of the trend line in slope-intercept form is:
y = -5x + 50