Question

hani sells postcards for $3 each. accounting for fixed costs, he sold 7 postcards for a net profit of $1. write an equation in point - slope form that represents this relationship.
show your work here
∘ $y - 1 = 3(x - 7)$ ∘ $y - 7 = 3(x - 1)$
∘ $y + 1 = 3(x + 7)$ ∘ $y + 7 = 3(x + 1)$

1. the graph of $f(x) = 2^x + 1$ represents the growth of a population of rabbits on a farm over x years. complete the sentence about the graph. the average rate of change for $1 \leq x \leq 5$ is...

Explanation:

Step1: Recall Point - Slope Form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify Slope and Point

• The slope $m$: Hani sells postcards for $\$3$ each. The profit per postcard sold is the slope of the profit - number of postcards sold line. So, the slope $m = 3$.
• The point $(x_1,y_1)$: He sold 7 postcards ($x_1 = 7$) for a net profit of $\$1$ ($y_1=1$).

Step3: Substitute into Point - Slope Form

Substitute $m = 3$, $x_1 = 7$ and $y_1=1$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 1=3(x - 7)$.

Answer:

A. $y - 1 = 3(x - 7)$