Answer:
The equation of the line is;
y = -x + 2
Step-by-step explanation:
Here, we want to find the equation of a line which is perpendicular to the given line and passes through the given point.
Mathematically;
If two lines are perpendicular, then , the slope of the two lines when multiplied by each other equals -1
The given line is;
y = x + 1
let’s compare this with the standard form which is y = mx + c
In the standard form, the coefficient of x is the slope. In this case, the coefficient of x is 1 and thus this is our slope
So the slope of the second line will be;
since m1 * m2 = -1
and m1 = 1
m2 = -1/1 = -1
The slope of the second line is -1
Now to get the equation of the second line; we use the point slope form
That would be;
y-y1 = m(x-x1)
The point (x1,y1) = (1, 1) and m = -1
Thus;
y-1 = -1(x -1)
y-1 = -x + 1
y = -x + 1 + 1
y = -x + 2 or simply y = 2-x
