Question

the graph represents the cost y (in dollars) to open an online gaming account and buy x games. write an equation in slope - intercept form that represents the graph. (there is a graph with x - axis labeled number of games and y - axis labeled cost (dollars), and a line plotted on it.)

Explanation:

Step1: Identify y-intercept

The y - intercept (\(b\)) is the value of \(y\) when \(x = 0\). From the graph, when \(x = 0\) (number of games is 0), \(y=15\). So \(b = 15\).

Step2: Calculate the slope

The slope (\(m\)) formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the graph. When \(x = 0,y = 15\) and when \(x = 1,y=30\) (we can see from the grid). Then \(m=\frac{30 - 15}{1 - 0}=\frac{15}{1}=15\).

Step3: Write the equation

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m = 15\) and \(b = 15\) into the formula, we get \(y = 15x+15\)? Wait, no, wait. Wait, when \(x = 0\), \(y = 15\), and when \(x = 1\), let's check the graph again. Wait, the y - axis is cost (dollars) and x - axis is number of games. Wait, maybe I misread the points. Let's take another pair. When \(x = 0\), \(y = 15\); when \(x = 1\), \(y = 30\)? Wait, no, the line goes from (0,15) to, say, (1,30)? Wait, no, the grid: each square is, let's see, x - axis: number of games, y - axis: cost. Let's take (0,15) and (1,30)? Wait, no, maybe (0,15) and (2,45)? Wait, no, let's calculate the slope correctly. Wait, the line: when \(x = 0\), \(y = 15\); when \(x = 1\), \(y = 30\)? Wait, no, the difference in y: from 15 to 30 is 15, difference in x: from 0 to 1 is 1. Wait, but let's check another point. When \(x = 2\), \(y = 45\). Then \(m=\frac{45 - 15}{2 - 0}=\frac{30}{2}=15\). So the slope is 15. Then the equation is \(y=15x + 15\)? Wait, no, wait, when \(x = 0\), \(y = 15\), so the y - intercept is 15, slope is 15. So the equation is \(y = 15x+15\)? Wait, but let's verify. If \(x = 0\), \(y = 15\) (correct). If \(x = 1\), \(y=15(1)+15 = 30\) (matches the graph). If \(x = 2\), \(y=15(2)+15 = 45\) (matches the graph). So the equation is \(y = 15x + 15\)? Wait, no, wait, maybe I made a mistake. Wait, the problem is about opening an account and buying games. The initial cost (account) is 15, and each game costs 15? That seems high, but according to the graph, the slope is 15 and y - intercept is 15. So the equation is \(y=15x + 15\). Wait, no, wait, let's re - examine the graph. Wait, the y - intercept is at (0,15), and the line goes up 15 for each 1 unit increase in x. So the slope is 15, y - intercept is 15. So the slope - intercept form is \(y=15x + 15\).

Answer:

\(y = 15x+15\)