Question

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: $y = 0x + 0$, $y = 30x + 0$, $y = 0x + 30$, $y = 30x + 30$. chart: total cost ($) on y - axis, number of months on x - axis. lines: $y = 30x + 20$ (climb time), $y = 30x$ (rock zone).

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 Rock Zone's graph

Looking at the graph for Rock Zone, when $x = 0$ (number of months is 0), the total cost $y$ is 0. So the $y$-intercept $b = 0$.
The slope $m$: For a linear relationship, if we take two points, say when $x = 1$, from the equation (or the graph trend), the cost $y$ should be 30 (since the line for Rock Zone is $y = 30x$). Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, taking $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1,30)$, we get $m=\frac{30 - 0}{1 - 0}=30$.

Step3: Write the equation

Substituting $m = 30$ and $b = 0$ into the slope - intercept form $y=mx + b$, we get $y=30x+0$ (or simplified as $y = 30x$). Looking at the options, $y = 30x+0$ is one of the given options.

Answer:

$y = 30x+0$ (or from the options, the correct equation for Rock Zone in slope - intercept form is $y = 30x+0$)