Use intercepts to graph the line described by each equation.
Problem 1 :
-x + 4y = 4
Problem 2 :
y = 2x - 4
Problem 3 :
2x + 3y + 6 = 0
Problem 4 :
y = 4x + 4
Problem 5 :
x + 4y = -4
Problem 6 :
-x + 2y = 4
Problem 7 :
The distance time graph shows Carloβs motion in front of a sensor.
a) Identify the d-intercept and explain what it means
b) Identify the t-intercept and explain what it means
c) Describe the instructions you would give someone walking in front of a sensor to reproduce this graph.
Problem 8 :
Consider the line
π₯ + 4π¦ = β4
To graph this line, you could:
a) determine the x- and y-intercepts
b) Create a table of values
c) use the equation to find the coordinates of three points on the line Which method of graphing do you prefer in this case? Explain.
1. Answer :
Find the intercepts.
x-intercept :
-x + 4y = 4
-x + 4(0) = 4
-x + 0 = 4
x = -4
(-4, 0)
y-intercept :
-x + 4y = 4
-0 + 4y = 4
4y = 4
y = 1
(0, 1)
Plot (-4, 0) and (0, 1).
Connect with a straight line.
2. Answer :
Find the intercepts.
x-intercept :
y = 2x - 4
0 = 2x - 4
4 = 2x
2 = x
(2, 0)
y-intercept :
y = 2x - 4
y = 2(0) - 4
y = 0 - 4
y = -4
(0, -4)
Plot (2, 0) and (0, -4).
Connect with a straight line.
3. Answer :
Find the intercepts.
x-intercept :
2x + 3y + 6 = 0
2x + 3(0) + 6 = 0
2x + 0 + 6 = 0
2x + 6 = 0
2x = -6
2x/2 = -6/2
x = -3
(-3, 0)
y-intercept :
2x + 3y + 6 = 0
2(0) + 3y + 6 = 0
0 + 3y + 6 = 0
3y + 6 = 0
3y = -6
3y/3 = -6/3
y = -2
(0, -2)
Plot (-3, 0) and (0, -2).
Connect with a straight line.
4. Answer :
Find the intercepts.
x-intercept :
y = 4x + 4
0 = 4x + 4
-4 = 4x
-1 = x
(-1, 0)
y-intercept :
y = 4x + 4
y = 4(0) + 4
y = 0 + 4
y = 4
(0, 4)
Plot (-1, 0) and (0, 4).
Connect with a straight line.
5. Answer :
Find the intercepts.
x-intercept :
x + 4y = -4
x + 4(0) = -4
x + 0 = -4
x = -4
(-4, 0)
y-intercept :
x + 4y = -4
0 + 4y = -4
4y = -4
y = -1
(0, -1)
Plot (-4, 0) and (0, -1).
Connect with a straight line.
6. Answer :
Find the intercepts.
x-intercept :
-x + 2y = 4
-x + 2(0) = 4
-x + 0 = 4
-x = 4
x = -4
(-4, 0)
y-intercept :
-x + 2y = 4
-0 + 2y = 4
0 + 2y = 4
2y = 4
y = 2
(0, 2)
Plot (-4, 0) and (0, 2).
Connect with a straight line.
7. Answer :
a) Approximately the d-intercept is 3.5, which means he is at 3.5 m distance from the motion sensor.
b) Here t-intercept is 7. Carol stops after 7 seconds.
c) Start at a distance of 3.5m from the motion sensor and walk at a constant speed of 0.5 m/s for 7s, then stop
8. Answer :
π₯ + 4π¦ = β4
To graph this line, you could:
a) determining the x- and y-intercepts :
x-intercept : Put y = 0 x + 4(0) = -4 x = -4 |
y-intercept : Put x = 0 0 + 4y = -4 4y = -4 y = -4/4 y = -1 |
x-intercept is (-4, 0) and y-intercept is (0, -1).
b)
When x = -1, π₯ + 4π¦ = β4 -1 + 4y = -4 4y = -4 + 1 4y = -3 y = -3/4 |
When x = 0 0 + 4π¦ = β4 4y = -4 y = -4/4 y = -1 |
When x = 1 1 + 4π¦ = β4 4y = -4 - 1 4y = -5 y = -5/4 |
When x = 2 2 + 4π¦ = β4 4y = -4 - 2 4y = -6 y = -6/4 y = -3/2 |
x -1 0 1 2 |
y -3/4 -1 -5/4 -3/2 |
(-1, -3/4) (0, -1) (1, -5/4) and (2, -3/2)
c.
To draw the graph, we can use two different ways.
i) graphing using intercepts :
x-intercept is (-4, 0) and y-intercept is (0, -1)
Joining above points, we get the straight line.
ii) Using slope intercept :
From the y-intercept -1, to get the next point we have to go 1 unit up and 4 units to the left. In the same way, we have to trace the other points and draw the straight line.
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