Answer/Step-by-step explanation:
✍️The equation of the line in point-slope form:
The equation is given as [tex] y - b = m(x - a) [/tex], where,
(a, b) = a point on the line.
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let's find the slope (m) of the line, housing (3, 21) and (6, 12):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 21}{6 - 3} = \frac{-9}{3} = -3 [/tex]
Substitute a = 3 and b = 21, m = -3 into [tex] y - b = m(x - a) [/tex].
Thus, the point-slope equation would be:
✅[tex] y - 21 = -3(x - 3) [/tex]
✍️The equation of the line in slope-intercept form:
Rewrite [tex] y - 21 = -3(x - 3) [/tex], so that y is made the subject of the formula.
[tex] y - 21 = -3x + 9 [/tex]
Add 21 to both sides
[tex] y = -3x + 9 + 21 [/tex]
[tex] y = -3x + 30 [/tex]
✅The slope-intercept equation of the line is [tex] y = -3x + 30 [/tex]
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)
