Question

ivan uses a transit card to pay for his bus fare. the table shows the amount of money left on the card, y, as a function of the number of rides ivan takes, x. write an equation to represent the amount of money left on the card, y. y = x + ? number of bus rides, x amount of money left on card ($), y 0 30 3 24 6 18 9 12

Explanation:

Step1: Find the slope

The slope $m$ of a linear - equation $y = mx + b$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(0,30)$ and $(x_2,y_2)=(3,24)$. Then $m=\frac{24 - 30}{3-0}=\frac{-6}{3}=-2$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 30$. So $b = 30$.

Answer:

$y=-2x + 30$