Question

one - time equipment fee when they sign up.
the equation $y = 30x + 20$ is
a linear equation. the equation is
in slope - intercept form.
$y = mx + b$
slope $y$ - intercept
how can you write the equation for
rock zone in slope - intercept form?
$y = 0x + 0$ $y = 0x + 30$
$y = 30x + 0$ $y = 30x + 30$
(chart: total cost ($) on y - axis, number of months on x - axis. two lines: $y = 30x + 20$ (climb time) starting at (0,20), $y = 30x$ (rock zone) starting at (0,0))

Explanation:

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: Determine the slope (\(m\)) and \(y\) - intercept (\(b\)) for Rock Zone

From the graph, the line for Rock Zone passes through the origin \((0,0)\), so the \(y\) - intercept \(b = 0\). Also, we can see that the slope \(m\) (the rate of change) is 30 (since for each increase of 1 in \(x\) (number of months), \(y\) (total cost) increases by 30, same as the other line's slope).

Step3: Write the equation

Using the slope - intercept form \(y=mx + b\), with \(m = 30\) and \(b=0\), the equation is \(y = 30x+0\).

Answer:

\(y = 30x + 0\) (among the options, this is the correct one. If we consider the options: the correct option is the one with \(y = 30x+0\))