An illustration of a scatterplot graph is titled Animal Longevity. It shows x-axis, labeled as average, ranging from 0 to 45 in increments of 5 and y-axis, labeled as maximum, ranging from 0 to 80 in increments of 10.

Question

Multiple points are plotted around a line that points upward to the right with an arrowhead on the top. The line passes approximately through (0, 20), (15, 40), (30, 60), and (40, 78). Two dotted lines are drawn forming a triangle under the line with the line being the hypotenuse. The dotted lines are drawn from (15, 40) to (30, 40) and from (30, 60) to (30, 40). 8 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

Answer 1

To find the equation of the trend line, we can use the two points that the line passes through: (0, 20) and (40, 78).

First, we'll find the slope of the line using the formula:

slope = (y2 - y1) / (x2 - x1)

slope = (78 - 20) / (40 - 0)
slope = 58 / 40
slope = 1.45

Next, we'll use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the given points.

We'll use the point (0, 20):

y - 20 = 1.45(x - 0)
y - 20 = 1.45x

Finally, we can rearrange the equation in slope-intercept form, y = mx + b, by isolating y:

y = 1.45x + 20

So the equation of the trend line in slope-intercept form is y = 1.45x + 20.