ted researched the price of airline tickets and discovered a correlation between the price of a ticket and…

ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. after recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. how can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? what does a positive correlation tell you about the dependent and independent variables?\na a positive correlation cannot be determined from examining an equation.\nb 300 is a positive y - intercept. the dependent and independent variables must be positive.\nc 300 is a positive x - intercept. the dependent and independent variables must be positive.\nd 0.45 is a positive slope. the dependent variable y increases as the independent variable x increases.

ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. after recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. how can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? what does a positive correlation tell you about the dependent and independent variables?\na a positive correlation cannot be determined from examining an equation.\nb 300 is a positive y - intercept. the dependent and independent variables must be positive.\nc 300 is a positive x - intercept. the dependent and independent variables must be positive.\nd 0.45 is a positive slope. the dependent variable y increases as the independent variable x increases.

Answer

Answer:

D. 0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.

Explanation:

Step1: Recall line - equation form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In $y = 300+0.45x$, $m = 0.45$ and $b = 300$.

Step2: Understand positive correlation

In a linear relationship $y=mx + b$, when $m>0$ (positive slope), as the value of the independent variable $x$ increases, the value of the dependent variable $y$ also increases. This indicates a positive correlation. Here, the slope $m = 0.45>0$, so there is a positive correlation between $x$ and $y$.