Question

data table: cost per bowl
components of linear
graphing: things to calculate
or establish as you develop
your graph. you may use
some, all, and other
information as well in your
writeup.
slope:1/14.95
meaning of slope 1 bowl of soup costs
$14,95
y - intercept none
meaning of y - intercept none
x - intercept
meaning of x - intercept
additional information you can gather:

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(1,14.95)\) and \((x_2,y_2)=(2,29.90)\). Then \(m=\frac{29.90 - 14.95}{2 - 1}=\frac{14.95}{1}=14.95\) (the given slope of \(\frac{1}{14.95}\) is incorrect). The meaning of the slope is that for each additional bowl of soup, the cost increases by \(14.95\) dollars.

Step2: Find the equation of the line

The equation of a line in slope - intercept form is \(y = mx + b\). Since when \(x = 0\), \(y=0\) (if \(x = 0\) bowls, cost \(y = 0\)), the \(y\) - intercept \(b = 0\). So the equation is \(y=14.95x\)

Step3: Find the \(x\) - intercept

To find the \(x\) - intercept, set \(y = 0\). Using the equation \(y=14.95x\), when \(y = 0\), we solve \(0=14.95x\), which gives \(x = 0\). The meaning of the \(x\) - intercept is that when the cost of soup bowls is \(0\) dollars, the number of soup bowls is \(0\)

Step4: Additional information

We can use the equation \(y = 14.95x\) to find the cost for any number of bowls. For example, if \(x=15\), then \(y=14.95\times15 = 224.25\) dollars. Also, the relationship is a direct proportionality (since \(y=kx\) where \(k = 14.95\) and \(b = 0\))

Answer:

• Slope: \(14.95\), meaning: cost per bowl of soup is \(\$14.95\)
• \(y\) - intercept: \(0\), meaning: cost is \(0\) when \(0\) bowls are bought
• \(x\) - intercept: \(0\), meaning: \(0\) bowls when cost is \(0\)
• Additional information: The relationship is \(y = 14.95x\) (direct proportion), can calculate cost for any \(x\) (number of bowls) using this formula.