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The two tables below show the amount of tipy, included on a bill charging x dollars.Restaurant ARestaurant B2550755101530which compares the slopes of the lines created by the tables?The slope of the line for Restaurant B is 3 times greater than the slope of the line for Restaurant A.The slope of the line for Restaurant Bis 2 times greater than the slope of the line for Restaurant AThe slope of the line for Restaurant Bis 5 times greater than the slope of the line for Restaurant AThe slope of the line for Restaurant Bis 10 times greater than the slope of the line for Restaurant ASave and ExitSubs

The Two Tables Below Show The Amount Of Tipy Included On A Bill Charging X DollarsRestaurant ARestaurant B2550755101530which Compares The Slopes Of The Lines Cr class=

Sagot :

A line can be represented by the following expression:

[tex]y\text{ = m}\cdot x\text{ + b}[/tex]

Where "m" is the slope of the line and "b" is the y-intercept. In this problem we only need to check the slope, so this is how we can calculate it:

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

Where (x1,y1) and (x2,y2) are two points that belong to that line.

To answer correctly we will calculate the slope of each restaurant using the points that were given on the table.

[tex]\begin{gathered} m_A\text{ = }\frac{3-1}{30-10}\text{ = }\frac{2}{20}\text{ = }\frac{1}{10} \\ m_B\text{ = }\frac{15-5}{75-25}=\frac{10}{50}\text{ = }\frac{1}{5} \end{gathered}[/tex]

To find how many times the slope of the line B is greater than the slope of the line B we need to divide mb by ma.

[tex]\begin{gathered} \text{ratio = }\frac{\frac{1}{5}}{\frac{1}{10}} \\ \text{ratio = }\frac{1}{5}\cdot\frac{10}{1} \\ ratio\text{ = }\frac{10}{5}\text{ = 2} \end{gathered}[/tex]

The slope of the line B is 2 times greater than the one of the line A. The correct option is the second one.

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