Q. 2 - Elementary Statistics

Question

Consider the linear equation $y=4-3x$.
a. At what $y-$value does its graph intersect the $y-$axis?

b. At what $x-$value does its graph intersect the $y-$axis?

c. What is its slope?

d. By how much does the $y-$value on the line change when the $x-$value increases by $1$ unit?

e. By how much does the $y-$value on the line change when the $x-$value decreases by $2$ units?

Step-by-Step Solution

Answer

The answers for the subparts have been given below.

Step 1. Given Information

The linear equation$y=4-3x$.

Step 2. The answer for (a)

The graph of the linear equation $y=4-3x$is as such:

In the above graph, we can see that $y=4$ the line intersects at the $y-$axis.

Step 3. The answer for (b)

At $x=0$ the line intersects the $y-$axis.

Step 4. The answer for (c)

The regression equation is $y=b_0+b_{1}x$
Here,
$b_0=y-$intercept
$b_1=$slope
$x=$independent variable
$y=$dependent variable
The given regression equation is $y=4-3x$
The slope,  width="59" height="25" style="max-width: none; vertical-align: -9px;" $b_1=-3$

Step 5. The answer for (d)

The $y-$value increases by $-3$ units for every increase in $x$ of $1$ unit.

Step 6. The answer for (e)

The $y-$value increases by $6$ units for every increase in $x$ of $2$ unit.