Question

If (1,13) and (3,7) are two anchor points on a trend line, then find the equation of the line.

Answer 1

Y = -3x + 16

Step-by-step explanation:

Slope of the line: (y-y)/(x-x)

(7-13)/(3-1) = -6/2 = -3

Point: (3,7)

y-y = m( x - x)

y - 7 = - 3(x - 3)

y - 7 = - 3x + 9

y = 3x + 9 + 7

y = -3x + 16

Answer 2

The equation of the line passing through the points (1,13) and (3,7) is calculated by first finding the slope using the two points, which is -3, and then using the slope and one point to find the y-intercept, resulting in the equation y = -3x + 16.

Step-by-step explanation:

To find the equation of the line that passes through two points, we'll start by determining the slope, which is change in y over the change in x (rise over run). The formula for the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1). Using the given anchor points (1, 13) and (3, 7), we can calculate the slope as follows:

m = (7 - 13) / (3 - 1) = -6 / 2 = -3.

Now that we have the slope, we can use one of the given points to find the y-intercept (b) using the point-slope formula: y - y1 = m(x - x1). Let's use the point (1, 13):

13 - y1 = -3(1 - x1)

13 = -3 + b

b = 13 + 3 = 16

Thus, the equation of the trend line is y = -3x + 16.