Which equation describes the line that passes through the point (5,1) and is perpendicular to the line 5x-4y=4

Question

Will someone teach me how to solve problems  this and this one? I need to know asap how to solve perpendicular and Parallel I totally forgot thanks! 

Answer 1

When two lines are perpendicular, the product of their slopes is equal to -1.

 

Therefore, if we know one slope, the other slope must be the negative reciprocal.

 

If one slope is 2/3, the other slope.must be -3/2

 

Let's look at this specific problem.

 

5x-4y =4

 

If we isolate y we can examine this line's slope.

 

-4y = -5x +4

 

y = 5/4x -1

 

The slope of this line is 5/4.

Therefore, as stated above, we need a line with a slope of -4/5

 

We can start by putting this line in slope intercept form.

 

y = mx+b.  We know m must be -4/5

 

y = -4/5x +b

 

Now solve for b by plugging in the ordered pair given (5,1)

1 = -4/5(5) + b

1 = -4 +b

5 = b

 

Our line needed is y=-4/5x+5