The two linear equations are:
1) y = -x + 5
2) y = (-1/2)*x - 1
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How to get the linear equations?</h3>
Remember that two linear equations are parallel if and only if have the same slope and different y-intercept.
So to find a linear equation:
y = m*x + b
Parallel to:
x + y = 4
y = -x + 4
The slope needs to be m = -1 and the y-intercept b ≠ 4
So our line will be:
y = -x + b
To find the value of b, we use the fact that this line passes through (2, 3), replacing the values of the point in the line we get:
3 = -2 + b
3 + 2 = b
5 = b
The linear equation is y = -x + 5
For the second case, we want to find a line perpendicular to:
2x - y = 5
y = 2x - 5
Two lines are perpendicular if the product of the slopes is -1, then:
m*2 = -1
m = -1/2
So the perpendicular line is something like:
y = (-1/2)*x + b
To find the value of b we use the fact that this line needs to pass through (6, -4)
Replacing these values we get
-4 = (-1/2)*6 + b
-4 = -3 + b
-4 + 3 =b
-1 = b
The line is:
y = (-1/2)*x - 1
Learn more about linear equations:
brainly.com/question/1884491
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