Question

1. this graph shows the amount of fabric in yards, f, that a designer needs to make p pairs of pants. which statement about this relationship is a lie? explain how you know. statement a: 1 pair of pants would require 2.5 yards of fabric. statement b: the line goes through the point (5, 8). statement c: 15 yards of fabric could make 6 pairs of pants.

Explanation:

Step1: Find the equation of the line

The line passes through the origin $(0,0)$ and the point $(2,5)$. The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=0,x_2 = 2,y_2 = 5$, so $m=\frac{5-0}{2 - 0}=\frac{5}{2}=2.5$. The equation of the line in slope - intercept form $y=mx + b$ (since $b = 0$ as it passes through the origin) is $y = 2.5p$, where $y$ is the amount of fabric and $p$ is the number of pairs of pants.

Step2: Check Statement A

For 1 pair of pants ($p = 1$), substituting $p=1$ into $y = 2.5p$, we get $y=2.5\times1 = 2.5$. So Statement A is true.

Step3: Check Statement B

Substitute $p = 5$ into $y=2.5p$. Then $y=2.5\times5=12.5
eq8$. So Statement B is a lie.

Step4: Check Statement C

If $y = 15$, then from $y = 2.5p$, we solve for $p$: $p=\frac{y}{2.5}=\frac{15}{2.5}=6$. So Statement C is true.

Answer:

Statement B is a lie because when $p = 5$ in the equation $y = 2.5p$ (derived from the relationship in the graph), $y=12.5$ not 8.