At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine which statement is true about the graph of the given equation:
[tex]\[ y + 4 = 4(x + 1) \][/tex]
we start by converting the equation into the slope-intercept form [tex]\( y = mx + b \)[/tex].
1. First, distribute the 4 on the right-hand side:
[tex]\[ y + 4 = 4x + 4 \][/tex]
2. Next, isolate [tex]\( y \)[/tex] by subtracting 4 from both sides:
[tex]\[ y = 4x + 4 - 4 \][/tex]
[tex]\[ y = 4x \][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = 4x \)[/tex]. This means the line has a slope of 4 and a y-intercept of 0. We will verify which set of points lies on this line.
### Checking each option:
- Option A: (1, -4) and (0, 0)
- Plugging [tex]\( x = 1 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(1) = 4 \][/tex]
This does not match with the point (1, -4).
- Plugging [tex]\( x = 0 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(0) = 0 \][/tex]
This matches with the point (0, 0), but since both points must satisfy the equation, this option is incorrect.
- Option B: (1, 4) and (2, 8)
- Plugging [tex]\( x = 1 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(1) = 4 \][/tex]
This matches with the point (1, 4).
- Plugging [tex]\( x = 2 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(2) = 8 \][/tex]
This matches with the point (2, 8), so this option is correct.
- Option C: (-4, -1) and (-3, -3)
- Plugging [tex]\( x = -4 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(-4) = -16 \][/tex]
This does not match with the point (-4, -1).
- Plugging [tex]\( x = -3 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(-3) = -12 \][/tex]
This does not match with the point (-3, -3), so this option is incorrect.
- Option D: (4, 1) and (5, 5)
- Plugging [tex]\( x = 4 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(4) = 16 \][/tex]
This does not match with the point (4, 1).
- Plugging [tex]\( x = 5 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(5) = 20 \][/tex]
This does not match with the point (5, 5), so this option is incorrect.
Since the correct option must satisfy the equation [tex]\( y = 4x \)[/tex] for both points given, the true statement about the graph is:
B. The graph is a line that goes through the points (1,4) and (2,8).
[tex]\[ y + 4 = 4(x + 1) \][/tex]
we start by converting the equation into the slope-intercept form [tex]\( y = mx + b \)[/tex].
1. First, distribute the 4 on the right-hand side:
[tex]\[ y + 4 = 4x + 4 \][/tex]
2. Next, isolate [tex]\( y \)[/tex] by subtracting 4 from both sides:
[tex]\[ y = 4x + 4 - 4 \][/tex]
[tex]\[ y = 4x \][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = 4x \)[/tex]. This means the line has a slope of 4 and a y-intercept of 0. We will verify which set of points lies on this line.
### Checking each option:
- Option A: (1, -4) and (0, 0)
- Plugging [tex]\( x = 1 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(1) = 4 \][/tex]
This does not match with the point (1, -4).
- Plugging [tex]\( x = 0 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(0) = 0 \][/tex]
This matches with the point (0, 0), but since both points must satisfy the equation, this option is incorrect.
- Option B: (1, 4) and (2, 8)
- Plugging [tex]\( x = 1 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(1) = 4 \][/tex]
This matches with the point (1, 4).
- Plugging [tex]\( x = 2 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(2) = 8 \][/tex]
This matches with the point (2, 8), so this option is correct.
- Option C: (-4, -1) and (-3, -3)
- Plugging [tex]\( x = -4 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(-4) = -16 \][/tex]
This does not match with the point (-4, -1).
- Plugging [tex]\( x = -3 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(-3) = -12 \][/tex]
This does not match with the point (-3, -3), so this option is incorrect.
- Option D: (4, 1) and (5, 5)
- Plugging [tex]\( x = 4 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(4) = 16 \][/tex]
This does not match with the point (4, 1).
- Plugging [tex]\( x = 5 \)[/tex] into [tex]\( y = 4x \)[/tex]:
[tex]\[ y = 4(5) = 20 \][/tex]
This does not match with the point (5, 5), so this option is incorrect.
Since the correct option must satisfy the equation [tex]\( y = 4x \)[/tex] for both points given, the true statement about the graph is:
B. The graph is a line that goes through the points (1,4) and (2,8).
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.