Question
Now, solve for b, or the vertical intercept. You can can substitute the x and y-values for a point on the line into the equation to help you. Solve on paper or use the calculator. Then, enter your answer on Zearn.
x
y
(4, 140)(8, 260)
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Time (minutes)
Elevation (meters)
y=30x+b
b=
x
y
(4, 140)(8, 260)
0
2
4
6
8
10
12
14
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
Time (minutes)
Elevation (meters)
y=30x+b
b=
Answers
GPT-4o mini
To find the vertical intercept \( b \) in the equation \( y = 30x + b \), you can use the coordinates of one of the points on the line. Let's use the point \( (4, 140) \).
Substituting \( x = 4 \) and \( y = 140 \) into the equation:
\[
140 = 30(4) + b
\]
Calculating \( 30(4) \):
\[
30(4) = 120
\]
So, we now have:
\[
140 = 120 + b
\]
To solve for \( b \), subtract 120 from both sides:
\[
b = 140 - 120
\]
\[
b = 20
\]
Thus, the vertical intercept \( b \) is:
\[
\boxed{20}
\]
Substituting \( x = 4 \) and \( y = 140 \) into the equation:
\[
140 = 30(4) + b
\]
Calculating \( 30(4) \):
\[
30(4) = 120
\]
So, we now have:
\[
140 = 120 + b
\]
To solve for \( b \), subtract 120 from both sides:
\[
b = 140 - 120
\]
\[
b = 20
\]
Thus, the vertical intercept \( b \) is:
\[
\boxed{20}
\]