Q. 5 - Elementary Statistics

Question

In Problems 3-5, answer true or false to each statement. Explain your answers.

If a line has a positive slope, $y-$values on the line decrease as the $x-$values decrease.

Step-by-Step Solution

Answer

It is true that if a line has a positive slope and its $y$-values drop as the $x$-values decrease.

Step 1: Concept Introduction

In a graph, if $y-$axis increases and $x-$ axis decreases, then they are positively related, and if $x$decreases, then $y$ declines as well. The slope of a line graph on a left-to-right axis is positive as the line moves from left to right.

Step 2: Explanation

The formula for slope is,

$$\begin{gathered} m=\frac{\text{ change in }y}{\text{ change in }x} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}$$

The slope of the line segment between $(2,5)$ and $(0,1)$ is:

Calculation of the slope is as follows: 

$$\begin{gathered} m=\frac{1-5}{0-2} \\ =2 \end{gathered}$$

Whenever any point on the line increases by $1, y$increases by $2$, and whenever any point on the line decreases by $1, y$decreases by $2$.