Question

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

Answer 1

Answer:

$y=-\frac{5}{2}x+\frac{45}{2}$

Step-by-step 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,

$y=-\frac{5}{2}x+c\\5=-\frac{5}{2}(7)+c\\5=-\frac{35}{2}+c\\c=5+\frac{35}{2}\\c=\frac{45}{2}$

Thus, the equation of perpendicular line is:

$y=-\frac{5}{2}x+\frac{45}{2}$