### The point (1;2) is on the line that is perpendicular to the line x+y-1=0. Determine the equation of the perpendicular line

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First, put the line x+y-1=0 into the slope intercept form

y= -x+1

Next, find the reciprocal of the slope, -1 and flip the sign.

-1 => 1/1 = 1

Next, put into point slope form of the perpendicular line using the point (1,2)

y-2 = 1(x-1)

and last, put this into slope intercept form (line equation)

y = x-1+2

**The equation of perpendicular line is y = x+1**

We know that 2 lines are perpendicular if the product of their slopes is -1.

We'll put the equation of the given line in the point slope form:

y = mx+n

For this reason, we'll keep y to the left side and we'll move the rest of terms to the right side:

y = -x + 1

Comparing, we'll get the slope of this line: m1 = -1

The slope of perpendicular line is m2 = -1/m1

m2 = -1/-1

m2 = 1

The equation of the perpendicular line, that has the slope m2 = 1 and it passes through the point (1;2) is:

y - 2 = 1*(x - 1)

y - 2 = x - 1

x - y - 1 + 2 = 0

x - y + 1 = 0

**The equation of the perpendicular line is:**

**x - y + 1 = 0**

The product of the slope of perpendicular lines is equal to -1.

The slope of x + y - 1 = 0 is -1, therefore the slope of the perpendicular line is 1.

As it passes through (1 , 2), (y - 2) / (x - 1) = 1

=> y - 2 = x - 1

=> x - y + 1 = 0

**The equation of the required line is x - y + 1 = 0**

The standard form of line equation can be calculated by following this formula. The formula is ( y - y1 ) = m ( x - x1 ) . Here m is called as slope. (x1, y1) is one of the point. The slope of formula can be calculated by following formula.The formula for slope is:

m = .

this is called as equation of line....

The product of the slope of perpendicular lines is equal to -1.

The slope of x + y - 1 = 0 is -1, therefore the slope of the perpendicular line is 1.

As it passes through (1 , 2), (y - 2) / (x - 1) = 1

=> y - 2 = x - 1

=> x - y + 1 = 0

The equation of the required line is x - y + 1 = 0

**m=(y2-y1)/(x2-x1) formula of slope derived from
equation of line**

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