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
\\(\circ\\ y - 1 = 3(x - 7)\\) \\(\circ\\ y - 7 = 3(x - 1)\\)\\(\bullet\\ y + 1 = 3(x + 7)\\) \\(\circ\\ y + 7 = 3(x + 1)\\)

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: Determine 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 $m = 3$ (since for each additional postcard sold, the profit increases by $\$3$).

Step3: Determine the Point $(x_1,y_1)$

We know that when he sold $x = 7$ postcards, the net profit $y=1$. So the point $(x_1,y_1)=(7,1)$.

Step4: Substitute into Point - Slope Form

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

Answer:

$y - 1 = 3(x - 7)$ (corresponding to the option "A. $y - 1 = 3(x - 7)$" if we consider the first option as A)