Math / Algebra

QuestionBeth has written her own recipe for pot roast. Her recipe says that a 2-pound roast should take 1 hour to cook. It also says that a 12-pound roast should take 6 hours to cook.
In this relationship, $x$ represents the weight (in pounds) of the pot roast, and $y$ represents the total cooking time (in hours).
Graph two points for this relationship and the line passing through them.

Studdy Solution

STEP 1

1. The relationship between the weight of the pot roast and the cooking time is linear.
2. We are given two data points: a 2-pound roast takes 1 hour to cook, and a 12-pound roast takes 6 hours to cook.
3. We need to graph these points and the line passing through them.

STEP 2

1. Identify the two points from the given information.
2. Plot the points on a coordinate plane.
3. Determine the equation of the line passing through these points.
4. Graph the line using the equation.

STEP 3

Identify the two points from the given information.
The first point is $(2, 1)$ , representing a 2-pound roast taking 1 hour. The second point is $(12, 6)$ , representing a 12-pound roast taking 6 hours.

STEP 4

Plot the points on a coordinate plane.
Place the point $(2, 1)$ on the graph, where the x-axis represents weight and the y-axis represents cooking time. Place the point $(12, 6)$ on the graph.

STEP 5

Determine the equation of the line passing through these points.
First, calculate the slope $m$ using the formula:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 1}{12 - 2} = \frac{5}{10} = \frac{1}{2}$
Now, use the point-slope form of the equation of a line $y - y_1 = m(x - x_1)$ with point $(2, 1)$ :
$y - 1 = \frac{1}{2}(x - 2)$
Simplify to get the equation in slope-intercept form:
$y = \frac{1}{2}x$

STEP 6

Graph the line using the equation.
Start at the y-intercept (0,0) since the line passes through the origin. Use the slope $\frac{1}{2}$ to plot additional points, moving up 1 unit and right 2 units from the origin. Draw the line through the points $(2, 1)$ and $(12, 6)$ .

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Studdy Solution

STEP 1

1. The relationship between the weight of the pot roast and the cooking time is linear.
2. We are given two data points: a 2-pound roast takes 1 hour to cook, and a 12-pound roast takes 6 hours to cook.
3. We need to graph these points and the line passing through them.

STEP 2

1. Identify the two points from the given information.
2. Plot the points on a coordinate plane.
3. Determine the equation of the line passing through these points.
4. Graph the line using the equation.

STEP 3

Identify the two points from the given information.
The first point is $(2, 1)$ , representing a 2-pound roast taking 1 hour. The second point is $(12, 6)$ , representing a 12-pound roast taking 6 hours.

STEP 4

Plot the points on a coordinate plane.
Place the point $(2, 1)$ on the graph, where the x-axis represents weight and the y-axis represents cooking time. Place the point $(12, 6)$ on the graph.

STEP 5

STEP 6

Graph the line using the equation.
Start at the y-intercept (0,0) since the line passes through the origin. Use the slope $\frac{1}{2}$ to plot additional points, moving up 1 unit and right 2 units from the origin. Draw the line through the points $(2, 1)$ and $(12, 6)$ .

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Studdy Solution

STEP 1

1. The relationship between the weight of the pot roast and the cooking time is linear.2. We are given two data points: a 2-pound roast takes 1 hour to cook, and a 12-pound roast takes 6 hours to cook.3. We need to graph these points and the line passing through them.

STEP 2

1. Identify the two points from the given information.2. Plot the points on a coordinate plane.3. Determine the equation of the line passing through these points.4. Graph the line using the equation.

STEP 3

Identify the two points from the given information.The first point is (2,1) (2, 1) (2,1), representing a 2-pound roast taking 1 hour. The second point is (12,6) (12, 6) (12,6), representing a 12-pound roast taking 6 hours.

STEP 4

Plot the points on a coordinate plane.Place the point (2,1) (2, 1) (2,1) on the graph, where the x-axis represents weight and the y-axis represents cooking time. Place the point (12,6) (12, 6) (12,6) on the graph.

STEP 5

STEP 6

Graph the line using the equation.Start at the y-intercept (0,0) since the line passes through the origin. Use the slope 12\frac{1}{2}21​ to plot additional points, moving up 1 unit and right 2 units from the origin. Draw the line through the points (2,1) (2, 1) (2,1) and (12,6) (12, 6) (12,6).

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The relationship between the weight of the pot roast and the cooking time is linear.
2. We are given two data points: a 2-pound roast takes 1 hour to cook, and a 12-pound roast takes 6 hours to cook.
3. We need to graph these points and the line passing through them.

1. Identify the two points from the given information.
2. Plot the points on a coordinate plane.
3. Determine the equation of the line passing through these points.
4. Graph the line using the equation.

Identify the two points from the given information.
The first point is $(2, 1)$ , representing a 2-pound roast taking 1 hour. The second point is $(12, 6)$ , representing a 12-pound roast taking 6 hours.

Plot the points on a coordinate plane.
Place the point $(2, 1)$ on the graph, where the x-axis represents weight and the y-axis represents cooking time. Place the point $(12, 6)$ on the graph.

Graph the line using the equation.
Start at the y-intercept (0,0) since the line passes through the origin. Use the slope $\frac{1}{2}$ to plot additional points, moving up 1 unit and right 2 units from the origin. Draw the line through the points $(2, 1)$ and $(12, 6)$ .