Fill in the blanks so that the following system of linear equations has infinite solutions.
y=2x+7
y=_____x+_______
y=2x+7
y=2x+7
For the system of linear equations to have infinite solutions, the second equation should be a multiple of the first equation. Therefore, the blanks can be filled in as follows:
y=2x+7
y=2x+7
so what is in the blanks
I apologize for the confusion. In the blank spaces, you can put any real number for both the coefficient of x and the constant term. Since any multiple of 2x+7 will be equal to 2x+7, you have infinite options to fill in the blanks. Here's an example:
y=2x+7
y=3(2x+7)
In this case, the second equation is a multiple of the first equation, and thus the system has infinite solutions.
bro wat y=______ x + _______
To have infinite solutions, the second equation should still be equal to the first equation. Therefore, the blanks can be filled in as follows:
y=2x+7
y=2x+7
Create a table that has 5 points that meets both of the following conditions:
the y-intercept is 5
the slope is 3
Explain how you know that the y-intercept is 5
Explain how you know that the slope is 3
To create a table of points that meet the given conditions, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Given that the y-intercept is 5, we can fill in the table as follows:
x | y
---------------
0 | 5
1 | 8
2 | 11
3 | 14
4 | 17
To explain why the y-intercept is 5, we can use the equation y = mx + b, where b represents the y-intercept. As stated, the equation has a slope of 3, so let's substitute a known point in the form (x, y) and solve for b:
Using the point (0, 5):
5 = 3(0) + b
5 = 0 + b
5 = b
b = 5
Therefore, the y-intercept is 5.
To explain why the slope is 3, we can observe the change in y divided by the change in x for different points:
For the points (0, 5) and (1, 8):
Change in y = 8 - 5 = 3
Change in x = 1 - 0 = 1
Slope = Change in y / Change in x = 3 / 1 = 3
This observation holds true for all the other points in the table as well, indicating that the slope is indeed 3.