Q.2 - Elementary Statistics

Question

Consider the linear equation $y=4-3 x$.

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

(a) at $y=4$, the provided equation's graph intersects the $y$ - axis.

(b) at $x=0$, the following equation's graph intersects the y - axis.

(c) slope $=-3$.

(d) the $y$ value changes. $3$  units

(e) change in  value  units.

Part (a)Step 1: Given information

Given in the question that,  Consider the linear equation $y=4-3 x$.

We need to find that at what $y$-value does its graph intersect the $y$-axis 

Part(a) Step 2: Explanation

Consider the $y=4-3 x$ equation.

When the graph crosses the $y$ - axis, $x=0$

$y=4-3\left(0\right)$

$y=4$

As a result, at $y=4$, the provided equation's graph intersects the $y$ - axis.

Part(b) Step 1: Given information

Given in the question that, Consider the linear equation $y=4-3 x$.

We need to find that at what $x$-value does its graph intersect the $y$-axis

Part (b) Step 2: Explanation

$y=4-3 x$is an equation.

Consider the $y=4-3 x$ equation.

When the graph crosses the $y$ - axis, $x=0$.

As a result, at $x=0$, the following equation's graph intersects the $y$ - axis.

Part(c) Step 1: Given information

Given in the question that, consider the linear equation $y=4-3 x$.

We need to find its slope.

Part(c) Step 2: Explanation

The formula $y=4-3 x$

Calculation:

Consider the $y=4-3 x$ equation.

Compare $y=m x+c$ 

$m=-3$

 to the above equation.

Thus, slope $=-3$.

Part(d) Step 1: Given information

Given in the question that, 

consider the linear equation $y=4-3 x$.

We need to find that by how much does the y-value on the line change when the $x$-value increases by 1 unit

Part (d) Step 2: Explanation

$y=4-3 x$ is an equation.

Consider the equation $y=4-3 x$ for a moment.

The equation's slope is $=-3$.

slope $=\frac{\text{ change in }y\text{-coordinates }}{\text{ changeinx-coordinates }}$

$-3=\frac{\text{ change in }\mathrm{y}\text{-coordinates }}{1}$

As a result, the $y$ value changes. $=3$ units

Part(e) Step 1: Given information

Given in the question that, consider the linear equation $y=4-3 x$.

We need to find that by how much does the $y$-value on the line change when the $x$-value decreases by 2 units?

Part (e) Step 2: Explanation

$y=4-3 x$ is an equation.

Consider the equation $y=4-3 x$ for a moment.

The equation's slope is $=-3$.

$=\frac{\text{ change in }y\text{-coordinates }}{\text{ changeinx-coordinates }}$

$-3=\frac{\text{ change in }\mathrm{y}\text{-coordinates }}{2}$

Change in y=$6$

As a result, the change in $y-$ value $=6$ units.