Question

1. austin went to the zoo. he paid $6 to get in and an additional $2 each time he rode the merry - go - round. this scenario can be represented by the function y = $6 + $2x. create a graph that models the amount of money austin spent at the zoo based on the number of times he rode the merry - go - round.

district formative assessment - extended response
algebra 1

Explanation:

Step1: Identify the slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given function $y=6 + 2x$, the slope $m = 2$ (the cost per ride) and the y - intercept $b = 6$ (the entry fee).

Step2: Choose points to plot

We can find points on the line by choosing values for $x$ (number of rides) and calculating the corresponding $y$ (total money spent). When $x = 0$, $y=6+2\times0=6$. When $x = 1$, $y=6 + 2\times1=8$. When $x = 2$, $y=6+2\times2 = 10$.

Step3: Plot the points and draw the line

Plot the points $(0,6)$, $(1,8)$, $(2,10)$ on the coordinate grid. Then draw a straight line through these points.

Answer:

To graph the function $y = 6+2x$:

1. Mark the point $(0,6)$ on the y - axis (since when $x = 0$, $y = 6$).
2. From the point $(0,6)$, use the slope of 2 (which means for every 1 unit increase in $x$, $y$ increases by 2 units). So, move 1 unit to the right and 2 units up to get the point $(1,8)$. Move 1 more unit to the right and 2 more units up to get the point $(2,10)$.
3. Draw a straight line passing through these points.