This graph represents the linear relationship between the time in minutes and the gallons of gas in the bus. For each minute, the gallons of gas increases at a constant rate. What do the points (4, 75) and (14, 175) represent?
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
The point (4, 75) means that after
minutes, there are
gallons of gas in the bus.
The point (14, 175) means that after
minutes, there are
gallons of gas in the bus.
Good work!
Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line? In other words, what is the change in gallons of gas for each minute?
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y= mx + b
Slope =
Nice!
Substitute the slope for m in our equation, or the rate of change of the gallons of gas.
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y= mx + b
y=
x+b
Slope = 10
Excellent!
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, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y=10x + b
b=
Good work!
Let’s finish writing our equation to represent the relationship between time and the gallons of gas in the bus. Now that we know the amount of gas in the bus when Corey started filling it, b, substitute the vertical intercept for b in our equation.
x
y
(4, 75)(14, 175)
0
2
4
6
8
10
12
14
16
18
20
0
25
50
75
100
125
150
175
200
Time (minutes)
Gallons of gas
y
=
10x + b
y
=
10x +
b
=
35
Great job!
Let’s use the equation to help us make a prediction. Remember x represents the time in minutes, and y represents the gallons of gas in the bus. How many gallons of gas will be in the bus after 18 minutes? Start by substituting 18 minutes for x in the equation.
y
=
10x
+
35
y
=
10
·
+
35
Nice!
Now, solve for y, the gallons of gas in the bus after 18 minutes.
y
=
10x
+
35
y
=
10·18
+
35
y
=
1 answer
To find the number of gallons of gas in the bus after 18 minutes, we will substitute \( x = 18 \) into the equation we established, which is:
\[ y = 10x + 35 \]
Now, substituting \( x = 18 \):
\[ y = 10(18) + 35 \]
Calculating that:
\[ y = 180 + 35 \]
\[ y = 215 \]
Therefore, after 18 minutes, there will be 215 gallons of gas in the bus.
1 answer
1 answer
1 answer
1 answer