Question

1) Tara's Verdant Veggies specializes in the sale of rare or unusual vegetable seeds. Tara sells packet of sweet-pepper seeds for $2.75 each and packet of rainbow blend tomato seeds for $4.25. You decided to buy these seeds at gifts for your friends. You spent a total of $46.75. a) From the scenario, write an equation: ________________________________ b) The y-intercept is _______________________ Show how you found the y-intercept: c) The x-intercept is _______________________ Show how you found the x-intercept: d) Graph the equation

Answer 1

We know that

• Each packet of sweet-pepper seeds costs $2.75.

,

• Each packet of rainbow blend tomato seeds costs $4.25.

,

• The total spending is $46.75.

Based on the given information, we can express the following equation

(a)

$2.75x+4.25y=46.75$

Where x refers to sweet-pepper seeds, and y refers to blend tomato seeds.

(b) To find the y-intercept, we solve the equation for y

$\begin{gathered} 4.25y=46.75-2.75x \\ y=\frac{46.75-2.75x}{4.25} \\ y=11-0.65x \end{gathered}$

The y-intercept is 11 because that's the constant.

(c) To find the x-intercept, we evaluate the equation for y = 0.

$\begin{gathered} 2.75x+4.25\cdot0=46.75 \\ 2.75x=46.75 \\ x=\frac{46.75}{2.75} \\ x=17 \end{gathered}$

The x-intercept is 17.

(d) The image below shows the graph