Find the parallel line for y=6x-2 ; (0,0)

Parallel Lines have the same slope so we take that slope and we put into our equation: y=6x-b

Then we find b by having everything equal b. So: b=-6x+y

Then we put our points into our equation: b=6*0+0  b=0

Now we go back to our original equation and put in our new b value.

y=6x+0

y

=

6

x

−

3

,  

(

0

,

9

)

Use the slope-intercept form to find the slope.

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m

=

6

To find an equation that is parallel to  

y

=

6

x

−

3

, the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

(

0

,

9

)

m

=

6

Find the value of  

b

using the formula for the equation of a line.

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b

=

9

Now that the values of  

m

(slope) and  

b

(y-intercept) are known, substitute them into  

y

=

m

x

+

b

to find the equation of the line.

y

=

6

x

+

9

Step-by-step explanation:

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step-by-step explanation:

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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!