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($) Cost of Candy Bar A Quantity 1 ($) Cost 1.25 2 2.50 3 3.75 4 5.00 5 6.25 The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y = x Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar A. Enter 2 for Candy Bar B. (1 point)

11 answers

To determine which candy bar is cheaper per unit, we need to find the cost per candy bar for both Candy Bar A and Candy Bar B.

Candy Bar A:

The cost for Candy Bar A is given in the table:

  • Quantity 1: $1.25 ā†’ Cost per bar = $1.25
  • Quantity 2: $2.50 ā†’ Cost per bar = $2.50/2 = $1.25
  • Quantity 3: $3.75 ā†’ Cost per bar = $3.75/3 = $1.25
  • Quantity 4: $5.00 ā†’ Cost per bar = $5.00/4 = $1.25
  • Quantity 5: $6.25 ā†’ Cost per bar = $6.25/5 = $1.25

For Candy Bar A, the cost per bar is consistently $1.25.

Candy Bar B:

The relationship for Candy Bar B is given by the equation \( y = x \). This means the cost is equal to the quantity (in dollars):

  • Quantity 1: $1.00 ā†’ Cost per bar = $1.00
  • Quantity 2: $2.00 ā†’ Cost per bar = $2.00/2 = $1.00
  • Quantity 3: $3.00 ā†’ Cost per bar = $3.00/3 = $1.00
  • Quantity 4: $4.00 ā†’ Cost per bar = $4.00/4 = $1.00
  • Quantity 5: $5.00 ā†’ Cost per bar = $5.00/5 = $1.00

For Candy Bar B, the cost per bar is consistently $1.00.

Conclusion:

Comparing the two:

  • Candy Bar A: $1.25 per bar
  • Candy Bar B: $1.00 per bar

Candy Bar B has the cheaper cost per bar.

So the answer is 2 for Candy Bar B.

What's the slope?
The plotted points are (0, -2) and (1, 3)

To find the slope of the line that passes through the two points \((0, -2)\) and \((1, 3)\), we use the formula for the slope \(m\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

  • \((x_1, y_1) = (0, -2)\)
  • \((x_2, y_2) = (1, 3)\)

Plugging in the values:

\[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]

Thus, the slope of the line is 5.

In slope-intercept form

The slope-intercept form of a linear equation is given by:

\[ y = mx + b \]

where \(m\) is the slope and \(b\) is the y-intercept.

From the previous calculation, we found that the slope \(m\) is \(5\). We also have the y-intercept from the point \((0, -2)\), which tells us that when \(x = 0\), \(y = -2\). Therefore, the y-intercept \(b\) is \(-2\).

Now we can substitute the values of \(m\) and \(b\) into the slope-intercept form:

\[ y = 5x - 2 \]

Thus, the equation in slope-intercept form is:

\[ y = 5x - 2 \]

(1, 3) and (0, -2) in slope-intercept form

To write the equation of the line that passes through the points \((1, 3)\) and \((0, -2)\) in slope-intercept form \(y = mx + b\), we will first find the slope \(m\) and then use one of the points to find the y-intercept \(b\).

Step 1: Find the slope \(m\)

Using the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (0, -2)\):

\[ m = \frac{-2 - 3}{0 - 1} = \frac{-5}{-1} = 5 \]

Step 2: Find the y-intercept \(b\)

Now that we have the slope \(m = 5\), we can use the y-intercept provided by point \((0, -2)\). Since when \(x = 0\), \(y = -2\), the y-intercept \(b\) is \(-2\).

Step 3: Write the equation in slope-intercept form

Now we can substitute the values of \(m\) and \(b\) into the slope-intercept form:

\[ y = mx + b \]

This gives us:

\[ y = 5x - 2 \]

Thus, the equation of the line in slope-intercept form that passes through the points \((1, 3)\) and \((0, -2)\) is:

\[ y = 5x - 2 \]

What's the clear answer

The equation of the line that passes through the points \((1, 3)\) and \((0, -2)\) in slope-intercept form is:

\[ y = 5x - 2 \]

Graph the linear equation y = 2x - 3

To graph the linear equation \(y = 2x - 3\), follow these steps:

1. Identify the slope and y-intercept

The equation is in slope-intercept form \(y = mx + b\) where:

  • \(m\) (slope) = 2
  • \(b\) (y-intercept) = -3

This means:

  • The slope of the line is 2, which indicates that for every 1 unit increase in \(x\), \(y\) increases by 2 units.
  • The y-intercept is \(-3\), meaning the line intersects the y-axis at the point (0, -3).

2. Plot the y-intercept

Start by plotting the y-intercept (0, -3) on the graph.

3. Use the slope to find another point

From the y-intercept (0, -3), apply the slope of 2:

  • Rise: 2 (go up 2 units)
  • Run: 1 (go right 1 unit)

Starting from (0, -3):

  • Move up 2 units to (1, -1)
  • Move right 1 unit to (1, -1)

Now, you have another point at (1, -1) to plot.

4. Draw the line

Using a ruler, draw a straight line through the points (0, -3) and (1, -1). Extend the line in both directions, adding arrows to indicate it continues infinitely.

Summary of Points

  • Start point: (0, -3)
  • Second point using slope: (1, -1)

You can also find additional points by substituting other values for \(x\) into the equation:

  • For \(x = 2\): \[ y = 2(2) - 3 = 4 - 3 = 1 \quad \implies (2, 1) \]
  • For \(x = -1\): \[ y = 2(-1) - 3 = -2 - 3 = -5 \quad \implies (-1, -5) \]

Graph

You will have points (0, -3), (1, -1), (2, 1), and (-1, -5) to plot, which will all lie on the same line.

Unfortunately, Iā€™m unable to create visual graphs directly, but you can use graphing software or graph paper to plot the points and draw the line based on the information provided.