Question

on a particular day, the value of 4 u.s. dollars is approximately equal to 3.50 euros, and 10 u.s. dollars is approximately equal to 8.72 euros. which equation shows the approximate value, in euros, as a function of u.s. dollars on this day? \\(\boldsymbol{y = 0.87x + 0.02}\\) \\(\boldsymbol{y = 0.87x + 3.50}\\) \\(\boldsymbol{y = 3.50x + 0.02}\\) \\(\boldsymbol{y = 3.50x + 0.87}\\)

Explanation:

Step1: Define variables

Let $x$ = U.S. dollars, $y$ = Euros. We use linear form $y=mx+b$.

Step2: Calculate slope $m$

Use points $(4, 3.50)$ and $(10, 8.72)$.
$$m=\frac{8.72-3.50}{10-4}=\frac{5.22}{6}=0.87$$

Step3: Solve for intercept $b$

Substitute $x=4$, $y=3.50$, $m=0.87$ into $y=mx+b$.
$$3.50=0.87(4)+b$$
$$3.50=3.48+b$$
$$b=3.50-3.48=0.02$$

Step4: Form the equation

Combine $m=0.87$ and $b=0.02$.
$$y=0.87x+0.02$$

Answer:

$y = 0.87x + 0.02$