Question

(a) What is the equation of the line, written in point-slope form? Show your work.

Step 1: Find the slope. m = y2 – y1 = _____- ____ = ______
x2 – x1 -
Step 2: Use point (4,15) and slope (m) from step 1 and complete the equation in point-slope form.
y-y1 = m (x-x1) y - _____ = _____ (x - ______)

Answer 1

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Explanation:

Answer 2

(a) The equation of the line, written in point-slope form is:

Step 1: Find the slope.
`(y_2-y_1)/(x_2-x_1)` =
`(9-15)/(8-4)` = -3/2.

Step 2: Use point (4,15) and slope (m) from step 1 and complete the equation in point-slope form.

`y - y_1 = m(x - x_1)` y - 15 = -3/2(x - 4)

(b) Step 1: At 0 days, Amy's sales time was 21 minutes.

Step 2: Amy’s sales time decreased 3/2 minutes per day.

(c) The equation in slope-intercept form is y = -3/2(x) + 21.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

`y - y_1 = m(x - x_1)`

Where:

• x and y represent the data points.
• m represent the slope.

Part a.

Step 1: First of all, we would determine the slope of this line by using these points (4, 15) and (8, 9);

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope (m) = (9 - 15)/(8 - 4)

Slope (m) = -6/4

Slope (m) = -3/2

Step 2.

At data point (4, 15) and a slope of -3/2, an equation for this line can be calculated by using the point-slope form as follows:

y - 15 = -3/2(x - 4)

Part b.

Based on the model, Amy's sales time was 21 minutes at 0 days. Hence, it initially took Amy 21 minutes to sell a cupcake. Also, Amy’s sales time decreased 3/2 minutes per day.

Part c.

Next, we would rewrite the equation Part (a) from point-slope form to slope-intercept form as follows;

y - 15 = -3/2(x - 4)

y = -3/2(x) + 6 + 15

y = -3/2(x) + 21

Complete Question:

Amy sells cupcakes. The graph shows a linear model for her sales times in minutes on different days.

(a) What is the equation of the line, written in point-slope form? Show your work.

Step 1: Find the slope.
`(y_2-y_1)/(x_2-x_1)` = _____- ____ = ______

Step 2: Use point (4,15) and slope (m) from step 1 and complete the equation in point-slope form.

`y - y_1 = m(x - x_1)` y - _____ = _____ (x - ______)

(b) Based on the model, how long did it initially take Amy to sell a cupcake? Approximately how much did her sales time decreased each day?

Step 1: At 0 days, what was her sales time? _________ minutes

Step 2: Amy’s sales time decreased ________ minutes per day

(c) Bonus: Rewrite the equation Part (a) from point-slope form to slope-intercept form.