Question

brian is tracking a plants height for his science class. when he begins tracking, the plant is 3 centimeters tall. the plant then grows 3 centimeters per week. let x be the time (in weeks) since brian started tracking the plants height, and let y be its height (in centimeters). (a) graph the line that shows the relationship between x and y. height (centimeters) time (weeks)

Explanation:

Step1: Find the linear - equation

The plant starts at a height of 3 cm and grows 3 cm per week. Using the slope - intercept form of a line $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, $m = 3$ (the growth rate per week) and $b = 3$ (the initial height). So the equation is $y=3x + 3$.

Step2: Find two points on the line

When $x = 0$:
$y=3\times0 + 3=3$. So the point is $(0,3)$.
When $x = 1$:
$y=3\times1+3 = 6$. So the point is $(1,6)$.

Step3: Plot the points and draw the line

Plot the points $(0,3)$ and $(1,6)$ on the coordinate plane. Then draw a straight line passing through these two points.

Since this is a graph - related task and we can't actually draw in this text - based format, the key steps to graph the line are described above.

Answer:

To graph the line $y = 3x+3$, plot the points $(0,3)$ and $(1,6)$ and draw a straight line through them.