Answer/Step-by-step explanation:
✍️The equation of the line in point-slope form:
The equation is given as
, where,
(a, b) = a point on the line.
![slope (m) = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%20slope%20%28m%29%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20)
Let's find the slope (m) of the line, housing (3, 21) and (6, 12):
![slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 21}{6 - 3} = \frac{-9}{3} = -3](https://tex.z-dn.net/?f=%20slope%20%28m%29%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%3D%20%5Cfrac%7B12%20-%2021%7D%7B6%20-%203%7D%20%3D%20%5Cfrac%7B-9%7D%7B3%7D%20%3D%20-3%20)
Substitute a = 3 and b = 21, m = -3 into
.
Thus, the point-slope equation would be:
✅![y - 21 = -3(x - 3)](https://tex.z-dn.net/?f=%20y%20-%2021%20%3D%20-3%28x%20-%203%29%20)
✍️The equation of the line in slope-intercept form:
Rewrite
, so that y is made the subject of the formula.
![y - 21 = -3x + 9](https://tex.z-dn.net/?f=%20y%20-%2021%20%3D%20-3x%20%2B%209%20)
Add 21 to both sides
![y = -3x + 9 + 21](https://tex.z-dn.net/?f=%20y%20%3D%20-3x%20%2B%209%20%2B%2021%20)
![y = -3x + 30](https://tex.z-dn.net/?f=%20y%20%3D%20-3x%20%2B%2030%20)
✅The slope-intercept equation of the line is ![y = -3x + 30](https://tex.z-dn.net/?f=%20y%20%3D%20-3x%20%2B%2030%20)
Where,
-3 = how much did his delivery time decrease per day (slope)
30 = how long it initially took Peter to deliver his packages (y-intercept)