The graph of f passes through (-4, 5) and is perpendicular to the line that has an x-intercept of 7 and a y-intercept of -49.

Question

The slope intercept form of the line is y=

 

I have tried this problem too many times and still cannot get the correct answer, according to my online math homework website.

Answer 1

So you are looking for a line perpendicular to a line that passes through the points (7,0) and (0,-49)

The slope of the line going through these points is:

m=(y₁-y₂)/(x₁-x₂)

m=(0-(-49))/(7-0)

m=49/7

m=7

 

Therefore the slope of the line you are looking for is -1/7.

Now we can use this slope and the given point (-4,5) to find the y-intercept (b)

y=mx+b

5=(-1/7)(-4)+b

5=4/7+b

b=31/7

 

Therefore, the equation of the line in point intercept form is:

y=-1/7x+31/7

 

Answer 2

First we have to find the slope of the original line, m=0-(-49)/7-0

 

m= 7

 

a perpendicular line will have opposite reciprocal slopes so our new slope will be m=-1/7

 

now we need y=mx+b

we have 5=-1/7(-4)+b

 

             5=4/7+b

 

             b=4 3/7

 

therefore y=-1/7x+ 4 3/7

Answer 3

First, we need to find this line with x-intercept of 7 and y-intercept of -49.  This line is our reference line.

 

The x-intercept is the value of x when y=0.

The y-intercept is the value of y when x=0.

 

The two points on this line to focus on are (7, 0)  and  (0, -49).

 

Next, we need to find the slope between these two points.

 

Slope = (-49 - 0) / (0 - 7)

Slope = -49 / -7

Slope = 7

 

 

So the equation of this line is          y = 7x - 49

 

 

Perpendicular lines have negative reciprocal slopes.  So the equation of the perpendicular so far is

 

y = (-1 / 7)x + b

 

 

This line passes through the point (-4, 5).  Plug in these values into the equation to find b.

 

5 = (-1 / 7)(-4) + b

 

5 = (4 / 7) + b

 

31 / 7 = b

 

 

The equation of the line we want is

 

y = (-1 / 7)x + (31 / 7)