Question

The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant's height at any time?
https://snag.gy/9d1b2U.jpg
A. y + 18 = 9(x + 2)
B. y - 18 = 9/2(x +2)
C. y - 18 = 9(x -2)
D. The relationship is nonlinear

Answer 1

@rebeccaxhawaii

Answer 2

First, we need to find the slope. What's the equation to calculate the slope given any two points?

Answer 3

I dont really know can you tell me?

Answer 4

Sure.
\[\huge m=\frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}\]
So take any two (x, y) points on the graph and plug them into that equation to calculate the slope throughout the whole graph. We know the slope is the same everywhere because if we were to plot the points and connect them, it would linear.

Answer 5

Yeah I know tat formula but I dont know it as a equation.

Answer 6

Okay one second I'll do that

Answer 7

Wait so is time x and the other is y?

Answer 8

And in one row there is only 2 numbers such as 2 and 18

Answer 9

Let's call Point 1 (2, 18) and Point 2 (4, 36). and plug these into our formula:

\[\huge m=\frac{36-18}{4-2}=\frac{18}{2}=9\]

Answer 10

From there, we can plug that into the point slope formula:

\[\huge y-y_0=m(x-x_0)\]

Answer 11

Where \((x_0, y_0)\) is any point on the graph.

Answer 12

And to answer your question from earlier, yes. Time is always on the x-axis.

Answer 13

Ohhh okay so what would be any point on the graph? would it be 54 and 72 for y and y0?

Answer 14

@sweetburger I know you you have helped me before :D

Answer 15

So time would be x and plant height would be y.

We can pick any two points to find the slope of the line
we would find the slope like this
\[m= \frac{ y_2-y_1 }{ x_2-x_1 }=\frac{ 36-18 }{4-2 } = \frac{ 18 }{ 2 } = 9\] so the slope of the line is 9.

Answer 16

Ohh okay that makes sense

Answer 17

Now we need to use the point-slope equation which is
\[y-y_1 = m(x-x_1)\] m which is the slope will be 9 and \[x_1\] can be any x value and \[y_1\] can be any y value.

Answer 18

Lets use the point (2,18) x=2 and y = 18. We know m which is the slope is 9. So we just plug in these values into the point slope equation.
\[y-18 = 9(x-2)\]

Answer 19

Thank you!!! That makes sense now.

Answer 20

np, Glad to help :)