Question

rock zone is a rock - climbing gym. members can pay for any number of months or part of a month. what is the equation of the line? $y = 1.5x$, $y = 3x$, $y = 15x$, $y = 30x$ (there is a chart with x - axis as number of months (from 0 to 4) and y - axis as total cost ($) (from 0 to 80), and a line starting from (0,0) going up.)

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and another point, for example, when \(x = 2\) (number of months), let's check the \(y\)-value (total cost). From the graph, when \(x = 2\), \(y = 60\)? Wait, no, wait. Wait, looking at the grid, each square: let's see, when \(x = 1\), what's \(y\)? Wait, maybe \(x = 2\), \(y = 60\)? Wait, no, maybe I misread. Wait, the \(y\)-axis is total cost in dollars, \(x\)-axis is number of months. Let's take \(x = 2\), \(y = 60\)? Wait, no, maybe \(x = 2\), \(y = 60\)? Wait, no, let's check the slope. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0,0)\) and \((2, 60)\)? Wait, no, maybe \((1, 30)\)? Wait, no, let's look again. Wait, the options are \(y = 1.5x\), \(y = 3x\), \(y = 15x\), \(y = 30x\). Let's take \(x = 2\), if \(y = 30x\), then \(y = 60\) when \(x = 2\). Wait, but let's check \(x = 1\): \(y = 30(1)=30\). Does the graph pass through \((1, 30)\)? Let's see the grid. The \(y\)-axis: 0, 20, 40, 60, 80. So at \(x = 1\), the line is at \(y = 30\)? Wait, no, maybe \(x = 2\), \(y = 60\). So slope \(m=\frac{60 - 0}{2 - 0}=30\)? Wait, no, that would be \(y = 30x\). Wait, but let's check another point. At \(x = 3\), \(y = 90\)? But the graph's top point is at \(x = 3\), \(y\) around 90? Wait, maybe I made a mistake. Wait, the options: \(y = 30x\) would mean when \(x = 1\), \(y = 30\); \(x = 2\), \(y = 60\); \(x = 3\), \(y = 90\). Let's check the graph. The line goes from (0,0) to, say, (2, 60)? Wait, no, the grid: each square is 20? Wait, no, the \(y\)-axis has 0, 20, 40, 60, 80. So between 0 and 20 is one square, 20 - 40 another, etc. So at \(x = 1\), the line is at \(y = 30\)? Wait, no, 30 is between 20 and 40. Wait, maybe \(x = 2\), \(y = 60\). So slope is 60/2 = 30. So the equation is \(y = 30x\)? Wait, no, wait, maybe I misread the graph. Wait, the options are \(y = 1.5x\), \(y = 3x\), \(y = 15x\), \(y = 30x\). Let's take \(x = 1\), if \(y = 30x\), then \(y = 30\). Does the graph pass through (1, 30)? Let's see: the line starts at (0,0), and at \(x = 1\), it's at \(y = 30\)? Wait, the \(y\)-axis is total cost, so maybe each month costs $30. So the equation is LXI58? Wait, no, wait, maybe LXI59, LXI60, so 60/2 = 30. So the slope is 30. So the equation is LXI61? Wait, but let's check the other options. LXI62 would be LXI63 when LXI64, LXI65 when LXI66, but the graph at LXI67 is at LXI68, so that's not. LXI69 would be LXI70 at LXI71, no. LXI72 even less. So the correct equation is LXI73? Wait, no, wait, maybe I messed up the LXI74 and LXI75 axes. Wait, LXI76 is number of months, LXI77 is total cost. So when LXI78 month, total cost LXI79 is $30? Then \(y = 30x\). Yes, that makes sense. So the slope is 30, so the equation is \(y = 30x\).

Step2: Verify with the options

The options are \(y = 1.5x\), \(y = 3x\), \(y = 15x\), \(y = 30x\). We found the slope is 30, so the equation is \(y = 30x\).

Answer:

\(y = 30x\)