Question

determine the slope and the y-intercept from the equation shown. * 1 point
$y = -\frac{1}{3}x + 4$
□ m= -1/3
□ m= -1/3x
□ m= 4
□ b= 4
□ b= -1/3x
□ b= -1/3
a community pool charges a flat fee of $2 to enter the pool and $3 per person. select the equation that best represents this situation.
○ y=2x-1
○ y=2x+1
○ y=3x-5
○ y=3x+2

Explanation:

First Sub - Question (Determine slope and y - intercept)

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Identify $m$ and $b$ from $y=-\frac{1}{3}x + 4$

Comparing $y =-\frac{1}{3}x+4$ with $y = mx + b$, we can see that $m=-\frac{1}{3}$ and $b = 4$.

Step1: Define variables

Let $x$ be the number of people and $y$ be the total cost.

Step2: Analyze the cost components

The flat fee is $2$ (this is the y - intercept, $b$) and the cost per person is $3$ (this is the slope, $m$).

Step3: Write the equation

Using the slope - intercept form $y=mx + b$, with $m = 3$ and $b = 2$, the equation is $y=3x + 2$.

Answer:

For the slope ($m$): m = - 1/3 (the first option)
For the y - intercept ($b$): b = 4 (the fourth option)

Second Sub - Question (Equation for pool charges)