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zlopas [31]
2 years ago
12

Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his delivery times on different

days. Peter’s Deliveries What is the equation of the line, first written in point-slope form, and then written in slope-intercept form? Show how you determined the equation. Based on the linear model, predict how long it initially took Peter to deliver his packages (y-intercept). Approximately how much did his delivery time decrease per day (slope)? Complete sentences.I need this done before Monday, please!

Mathematics
1 answer:
aev [14]2 years ago
5 0

Answer/Step-by-step explanation:

✍️The equation of the line in point-slope form:

The equation is given as y - b = m(x - a), where,

(a, b) = a point on the line.

slope (m) = \frac{y_2 - y_1}{x_2 - x_1}

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

Substitute a = 3 and b = 21, m = -3 into y - b = m(x - a).

Thus, the point-slope equation would be:

✅y - 21 = -3(x - 3)

✍️The equation of the line in slope-intercept form:

Rewrite y - 21 = -3(x - 3), so that y is made the subject of the formula.

y - 21 = -3x + 9

Add 21 to both sides

y = -3x + 9 + 21

y = -3x + 30

✅The slope-intercept equation of the line is y = -3x + 30

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)

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