Question

Perpendicular to the line 2x-5y=-11; passes through (7,5)

Answer 1

`y=-(5)/(2)x+(45)/(2)`

Explanation:

The slope intercept form of a line is given as:

y = mx + c

Where m is the slope and c is the y-intercept

Let's rearrange the equation given in this form:

2x - 5y = -11

5y = 2x + 11

y = 2/5 x + 11/5

So the slope is 2/5

Slope of line that is perpendicular to this is the "negative reciprocal" of this slope. Which means the slope of perpendicular line would be -5/2

Thus, equation would become: y = -5/2x + c

Now we need to find c. For this we plug in 7 into x and 5 into y and solve for c [(7,5) is the point given]. Thus,

`y=-(5)/(2)x+c\\5=-(5)/(2)(7)+c\\5=-(35)/(2)+c\\c=5+(35)/(2)\\c=(45)/(2)`

Thus, the equation of perpendicular line is:

`y=-(5)/(2)x+(45)/(2)`