To find the equation of the line through the given points, we first need to calculate the slope of the line using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
1. For the points (8, 10) and (14, 13):
m = (13 - 10) / (14 - 8)
m = 3 / 6
m = 0.5
Next, we can choose one of the points, let's say (8, 10), and substitute the slope into the slope-intercept form equation: y = mx + b. Using point-slope form, we have:
10 = 0.5(8) + b
10 = 4 + b
b = 10 - 4
b = 6
Therefore, the equation of the line through the points (8, 10) and (14, 13) is y = 0.5x + 6.
2. For the points (5, 17) and (9, 5):
m = (5 - 17) / (9 - 5)
m = -12 / 4
m = -3
Using point-slope form with point (5, 17):
17 = -3(5) + b
17 = -15 + b
b = 17 + 15
b = 32
Thus, the equation of the line through the points (5, 17) and (9, 5) is y = -3x + 32.
