for two variables $x$ and $y$, the value of $y$ decreases by 2 units whenever the value of $x$ increases by…

for two variables $x$ and $y$, the value of $y$ decreases by 2 units whenever the value of $x$ increases by 1 unit. further, the value of $y$ is 3 whenever $x = 0$. explain how to derive the equation that represents the relationship between these two variables, and state the equation.

for two variables $x$ and $y$, the value of $y$ decreases by 2 units whenever the value of $x$ increases by 1 unit. further, the value of $y$ is 3 whenever $x = 0$. explain how to derive the equation that represents the relationship between these two variables, and state the equation.

Answer

Explanation:

Step1: Identify slope (rate of change)

Since $y$ decreases by 2 when $x$ increases by 1, the slope $m = -2$.

Step2: Identify y-intercept

When $x=0$, $y=3$, so the y-intercept $b = 3$.

Step3: Use slope-intercept form

The slope-intercept equation of a line is $y = mx + b$. Substitute $m=-2$ and $b=3$. <Expression> $y = -2x + 3$ </Expression>

Answer:

The relationship follows the slope-intercept form of a linear equation. The slope is determined by the constant rate of change of $y$ with respect to $x$, and the y-intercept is given by the value of $y$ when $x=0$. Substituting these values into $y=mx+b$ gives the final equation: $\boldsymbol{y = -2x + 3}$