y = -2x + 1
y – [ ] = [ ] ( x – [ ] )
y – 1 = -2( x – 0 )
To fill in the blanks in the given expression "y – [ ] = [ ] ( x – [ ] )", we can use the equation y = -2x + 1.
First, let's determine the values to fill in the blanks.
1. The coefficient of x in the equation y = -2x + 1 is -2. This will be the value we fill in the first set of blanks: [ -2 ].
2. The constant term in the equation y = -2x + 1 is 1. This will be the value we fill in the second set of blanks: [ 1 ].
3. The sign before the x term is a negative sign. This will be the value we fill in the third set of blanks: [ - ].
Now, let's substitute these values into the expression:
y – [ -2 ] = [ 1 ] ( x – [ - ] )
So, the complete expression becomes:
y - (-2) = 1(x - (-))
Simplifying further, we have:
y + 2 = 1(x + )
Finally, the filled-in expression is:
y + 2 = 1(x + ).
To complete the expression y – [ ] = [ ] ( x – [ ] ), we need to find the missing values. Let's break down the given equation y = -2x + 1 to identify the missing values.
In the equation y = -2x + 1, we have:
- The coefficient of x: -2
- The constant term: 1
Now, let's replace the missing values in the expression y – [ ] = [ ] ( x – [ ] ):
1. The missing value in the first set of brackets should be the negative of the constant term in the given equation. Therefore, it is -1.
So far, the expression becomes y – (-1) = [ ] ( x – [ ] ):
2. The missing value in the second set of brackets should be the reciprocal of the coefficient of x in the given equation. The reciprocal of -2 is -1/2.
Now, the complete expression is y – (-1) = ( -1/2 ) ( x – [ ] ):
To find the final missing value, we need to determine the x-coordinate of a point that lies on the line represented by the given equation y = -2x + 1. Let's choose a value for x and solve for y:
Let x = 2:
y = -2(2) + 1
y = -4 + 1
y = -3
Therefore, when x = 2, y = -3. We can substitute these values into the expression:
-3 – (-1) = ( -1/2 ) ( x – [ ] )
-3 + 1 = ( -1/2 ) ( x – [ ] )
-2 = ( -1/2 ) ( x – [ ] )
To find the final missing value, we need to solve for x. Let's rearrange the equation:
-2 = ( -1/2 ) ( x – [ ] )
-2 = ( -x/2 ) + ( [ ]/2 )
Simplify the equation:
-4 = -x + [ ]
-4 + x = [ ]
Therefore, the final missing value in the expression is -4 + x.
The complete expression is y – (-1) = ( -1/2 ) ( x – (-4 + x) )