The equation of line qr is x + 2y = 2. what is the equation of a line perpendicular to line qr in slope-intercept form that contains point (5, 6)?
y = negative one halfx + seventeen halves
y = 2x − 4
y = negative one halfx + seven halves
y = 2x + 16

y=2x-4

Step-by-step explanation:

step 1

Find the slope of the line QR

we have

x+2y=2

isolate the variable y

2y=-x+2

y=-(1/2)x+1

The slope m is equal to

m=-1/2

step 2

Find the slope of the line perpendicular to line QR

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

m1*m2=-1

we have

m1=-1/2

substitute

(-1/2)*m2=-1

m2=2

The slope of the line perpendicular to line QR is m=2

step 3

Find the equation of the line into slope intercept form

The equation of the line is equal to

y=mx+b

we have

m=2

point (5,6)

substitute and solve for b

6=(2)(5)+b

6=10+b

b=6-10

b=-4

The equation is equal to

y=2x-4

hi! i think the answer is 1/2 : )

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!