To represent the relationship between time and Thomas’s elevation, a linear equation can be written in the form y=mx+b. Substitute the slope for m in our equation.

Question

x
y
(3, 1,600)(7, 3,600)
0
1
2
3
4
5
6
7
8
9
10
0
400
800
1,200
1,600
2,000
2,400
2,800
3,200
3,600
4,000
4,400
Time (hours)
Elevation (meters)
y= mx + b
y=
x+b

Slope = 500

Answer 1

To write the linear equation in the form \(y = mx + b\), we have the slope \(m = 500\).

To find the linear equation, we also need the y-intercept \(b\). We know two points on the line: \((3, 1600)\) and \((7, 3600)\).

Using the slope-intercept form, we can substitute \(m\) and one of the points to find \(b\).

Let's use the point \((3, 1600)\):

\[ y = mx + b \]

Substituting in the values:

\[ 1600 = 500(3) + b \]

Calculating \(500(3)\):

\[ 1600 = 1500 + b \]

Now, solve for \(b\):

\[ b = 1600 - 1500 \]

\[ b = 100 \]

Now that we have both \(m\) and \(b\), we can write the complete equation:

\[ y = 500x + 100 \]

So, the equation representing the relationship between time \(x\) (in hours) and Thomas’s elevation \(y\) (in meters) is:

\[ y = 500x + 100 \]