"find the equation of the line passing through the point (1,1) and perpendicular to the line y=5x-1 enter the exact answer. use improper fractions if it is necessary, do not use mixed fractions."

In this question, we have o find the equation of line passing through point (1,1) and is perpendicular to the line

And slope of the given line is 5. And slopes of perpendicular lines are opposite and reciprocal of each other.

So slope of perpendicular line is

Using slope intercept form, which is

Substituting the values of x and y from the given point, and the value of m, we will get

adding 1/5 to both sides

So the required equation of line is

The equation of the perpendicular line will be:

Explanation

Given equation of the line :

After comparing the above equation with slope intercept form , we will get:  Slope = 5

As the slope of a perpendicular line is negative reciprocal of the slope of given line, so here the slope of the perpendicular line will be:

Now, the perpendicular line have slope as and it's passing through the point = , so using the point-slope form......

So, the equation of the perpendicular line will be:

the answer is 5/14.

hope this .

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