Question

Write the equations of the following lines.

b
The line is perpendicular to the graph of y=x+1 and passes through the point (1,1).

Answer 1

The equation of the line is;

y = -x + 2

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