what does the y intercept represent on a graph

2.7: Interpreting the y-tap of a Line

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19636

Learning Outcomes

1. Understand the \(y\)-wiretap of a line Eastern Samoa the value of \(y\) when \(x\) equals to 0.
2. Determine whether the \(y\)-intercept is useful for interpreting the relationship betwixt \(x\) and \(y\)

Just like the slope of a subscriber line, many algebra classes go over the y-intercept of a line without explaining how to practice it in the literal macrocosm. The y-bug of a line is the value of \(y\) where the line crosses the y-axis. Put differently, information technology is the value of \(y\) when the time value of \(x\) is adequate to 0. Sometimes this has true meaning for the theoretical account that the agate line provides, but other times it is meaningless. We will encounter examples of both types in this section.

Example \(\PageIndex{1}\)

A study was done to see the relationship between the ounces of meat, \(x\), that people eat each Clarence Day on average and the hours per week, \(y\) they watch sports. The equation of the regression product line was found to follow:

\[y=1.3\:+0.4x\nonumber \]

Construe with the y-intercept of the regression line in the linguistic context of the study or explain wherefore it has no more practical meaning.

Solution

First off, note that the y-intercept is the figure that is not ahead of the \(x\). Thus, the y-intercept is 1.3. Following, the y-wiretap is the value of \(y\) when \(x\) equals zero. For this example, \(x\) represents the ounces of meat exhausted each daytime. If \(x\) is equal to 0, this means the somebody does not consume any meat. Since there are citizenry, called vegetarians, who devour atomic number 102 meat, it is meaningful to have an x-value of 0. The y-value of 1.3 represents the hours of sports the person watches. Putting this all together we can state:

A vegetarian is predicted to watch 1.3 hours of sports every week.

Object lesson \(\PageIndex{2}\)

A baby nurse at Children's Hospital has collected information on the birth weight, \(x\), in pounds the number of days, \(y\), that the newborns stay in the hospital. The equation of the regression line was found to be

\[y=45\:-3.9x\nonumber \]

Interpret the y-intercept of the regression line in the context of the subject field or explain wherefore it has no possible meaning.

Solution

Again, we note that the y-intercept is the total that is not in front of the \(x\). Thus, the y-intercept is 45. Next, the y-intercept is the value of \(y\) when \(x\) equals zero. For this illustration, \(x\) represents the new born baby's parentage weight in pounds. If \(x\) is equal to 0, this substance the baby was born with a weight of 0 pounds. Since it makes No sense for a featherbed to weigh 0 pounds, we can say that the y-intercept of this regression line has no practical meaning.

Case \(\PageIndex{3}\)

A researcher asked single mass "How many cups of coffee did you toast last week?" and "How many times did you go to a shop or restaurant for a meal or a salute last week?" The scatterplot and the regression line from this study are shown below.

Interpret the y-tap of the regression line in the circumstance of the study operating theater explain why it has no practical meaning.

Solution

The y-intercept of a pipeline is where it crosses the y-bloc. In this case, the line crosses at around y = -1. The value of \(x\), by definition is 0 and the x-Axis represents the number of cups of burnt umber a person drank endure week. Since there are people World Health Organization assume't wassail coffee, it does male sense to give birth an x-assess of 0. The y-axis represents the count of times the person went to a give away or restaurant last week to purchase a meal or a drink. IT makes no sense to enunciat that a person went -1 times to a shop or restaurant last week to purchase a meal or a potable. Consequently the y-intercept of this regression toward the mean line has nobelium practical meaning.

Exercise

The scatterplot and regression line below are from a study that collected data from a group of college students on the bi of hours per week during the civilis year they work at a paid problem and the number of units they are pickings. Interpret the y-intercept of the regression line or explain wherefore it has nobelium practical meaning.

• Interpret the Meaning of the y-wiretap Given a Linear Par
• Rendition the y-Intercept

what does the y intercept represent on a graph

Source: https://math.libretexts.org/Courses/De_Anza_College/Pre-Statistics/2:_Graphing_Points_and_Lines_in_Two_Dimensions/2.7:_Interpreting_the_y-intercept_of_a_Line