Question

climb time is a different rock - climbing gym. it also costs $30 per month, but new members pay a 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? options: $y = 0x + 0$, $y = 0x + 30$, $y = 30x + 0$, $y = 30x + 30$. there is a chart with $x$ as number of months and $y$ as total cost ($). the lines are $y = 30x + 20$ (climb time) and rock zone $y = 30x$.

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: Analyze the graph for Rock Zone

From the graph, the line for Rock Zone passes through the origin \((0,0)\), so the \(y\) - intercept \(b = 0\). Also, the slope \(m\) for Rock Zone: we know that for the equation \(y = 30x\) (from the graph label), the slope \(m = 30\) (since the equation of Climb Time is \(y=30x + 20\) with slope 30, and the line for Rock Zone is parallel to it, so they have the same 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:

\(y = 30x + 0\)