To solve the system of equations using a graphical method, we need to plot the graphs of the two equations and determine the point where they intersect, since that point represents the solution to the system.
First, let's plot the graph of y = 3x - 5. This is a linear equation in slope-intercept form, where the slope is 3 and the y-intercept is -5. To graph it, we can plot two points and draw a line through them.
To find the x-intercept, set y = 0:
0 = 3x - 5
3x = 5
x = 5/3 ≈ 1.67
To find the y-intercept, set x = 0:
y = 3(0) - 5
y = -5
So, we have two points: (0,-5) and (5/3,0). Let's plot them:
Next, let's plot the graph of y = 13x + 3. Again, this is a linear equation in slope-intercept form, where the slope is 13 and the y-intercept is 3. To graph it, we can plot two points and draw a line through them.
To find the x-intercept, set y = 0:
0 = 13x + 3
13x = -3
x = -3/13 ≈ -0.23
To find the y-intercept, set x = 0:
y = 13(0) + 3
y = 3
So, we have two points: (0,3) and (-3/13,0). Let's plot them:
Now, we can see that the two lines intersect at the point (4,3). Therefore, the solution to the system of equations is x = 4 and y = 3.
The correct answer is A) (4, 3).
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Question
Solve the system of equations y = 3x - 5 and y = 13
x + 3 using a graphical method.
Responses
A (4, 3)(4, 3)
B (3, 4)(3, 4)
C (0, 3)(0, 3)
D (0, -5)5 of 205 of 20 Items
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Question
Solve the system of equations y = 3x - 5 and y = 13
x + 3 using a graphical method.
Responses
A (4, 3)(4, 3)
B (3, 4)(3, 4)
C (0, 3)(0, 3)
D (0, -5)
5 answers
Domain Test
Question Id : 317163
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Question
Rectangle CDEF undergoes a dilation centered at the origin. The result is rectangle C'D'E'F'. Which rule describes the dilation?
Responses
A (x, y) → (2x, 2y)(x, y) → (2x, 2y)
B (x, y) → (4x, 4y)(x, y) → (4x, 4y)
C (x, y) → (−12
x, −12
y)(x, y) → (− 1 2 x, − 1 2 y)
D (x, y) → (12
x, 12
y)
Question Id : 317163
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Question
Rectangle CDEF undergoes a dilation centered at the origin. The result is rectangle C'D'E'F'. Which rule describes the dilation?
Responses
A (x, y) → (2x, 2y)(x, y) → (2x, 2y)
B (x, y) → (4x, 4y)(x, y) → (4x, 4y)
C (x, y) → (−12
x, −12
y)(x, y) → (− 1 2 x, − 1 2 y)
D (x, y) → (12
x, 12
y)
To determine the rule that describes the dilation of rectangle CDEF to C'D'E'F', we need to analyze the changes in the coordinates of the vertices.
A dilation is a transformation that changes the size of a shape while preserving its shape and proportions. In this case, we can see that the dilation of rectangle CDEF results in a rectangle that is larger.
Let's focus on one vertex of the rectangle, such as vertex C. The coordinates of vertex C are (x, y).
Based on the dilation, the x-coordinate is doubled, and the y-coordinate is also doubled. This is because the dilation is centered at the origin, so the origin (0,0) remains the same.
Therefore, the rule that describes the dilation is A) (x, y) → (2x, 2y). This means that the x-coordinate and y-coordinate of each vertex of the original rectangle are multiplied by 2 to determine the coordinates of the corresponding vertex in the dilated rectangle.
The correct answer is A) (x, y) → (2x, 2y).
A dilation is a transformation that changes the size of a shape while preserving its shape and proportions. In this case, we can see that the dilation of rectangle CDEF results in a rectangle that is larger.
Let's focus on one vertex of the rectangle, such as vertex C. The coordinates of vertex C are (x, y).
Based on the dilation, the x-coordinate is doubled, and the y-coordinate is also doubled. This is because the dilation is centered at the origin, so the origin (0,0) remains the same.
Therefore, the rule that describes the dilation is A) (x, y) → (2x, 2y). This means that the x-coordinate and y-coordinate of each vertex of the original rectangle are multiplied by 2 to determine the coordinates of the corresponding vertex in the dilated rectangle.
The correct answer is A) (x, y) → (2x, 2y).
Porportional relationship
A proportional relationship is a relationship between two variables in which their ratios remain constant. In other words, when one variable increases or decreases, the other variable changes in direct proportion.
For example, consider the relationship between the number of hours worked and the amount earned. If someone earns $10 per hour, the relationship between the number of hours worked (x) and the amount earned (y) can be represented as y = 10x. In this case, the ratio of the amount earned to the number of hours worked remains constant at $10 per hour.
Another example is the relationship between distance and time when traveling at a constant speed. If you are traveling at a speed of 60 miles per hour, the relationship between the distance traveled (x) and the time taken (y) can be represented as y = 60x. Again, the ratio of the distance traveled to the time taken remains constant at 60 miles per hour.
In a proportional relationship, if you were to graph the relationship, the points would lie on a straight line that passes through the origin (0,0). Additionally, the equation representing the relationship would be in the form y = kx, where k is the constant of proportionality.
It's important to note that not all relationships are proportional. In a non-proportional relationship, the ratios between the variables do not remain constant as one variable changes.
Understanding proportional relationships can be helpful in various real-life scenarios, such as calculating rates, scaling objects, determining unit rates, and analyzing linear relationships.
For example, consider the relationship between the number of hours worked and the amount earned. If someone earns $10 per hour, the relationship between the number of hours worked (x) and the amount earned (y) can be represented as y = 10x. In this case, the ratio of the amount earned to the number of hours worked remains constant at $10 per hour.
Another example is the relationship between distance and time when traveling at a constant speed. If you are traveling at a speed of 60 miles per hour, the relationship between the distance traveled (x) and the time taken (y) can be represented as y = 60x. Again, the ratio of the distance traveled to the time taken remains constant at 60 miles per hour.
In a proportional relationship, if you were to graph the relationship, the points would lie on a straight line that passes through the origin (0,0). Additionally, the equation representing the relationship would be in the form y = kx, where k is the constant of proportionality.
It's important to note that not all relationships are proportional. In a non-proportional relationship, the ratios between the variables do not remain constant as one variable changes.
Understanding proportional relationships can be helpful in various real-life scenarios, such as calculating rates, scaling objects, determining unit rates, and analyzing linear relationships.
8 answers