Graph the lines y=4*+2 and y=-x+7 on the graph below then find their point of intersection and record the solution

The Graph for Both is attached below.,

For line , y = 4x + 2 ......Red color Line on Graph

For line , y = -x + 7 ............Purple color Line on Graph.

Point of Intersection is ( 1 , 6 )  ....Orange Color

Step-by-step explanation:

Assume, y = 4x+2

Given:

For y = 4x + 2

Let the points be point A, and point B  

To Find:

Point of Intersection  of Two given lines= ?

Solution:

For Drawing a graph we require minimum two points but we will have here three points.

For y = 4x + 2

For point A( x₁ , y₁)

Put x = 0 in the given equation we get

y=4(0) + 2 =2

y=2

∴ y = 2

∴ point A( x₁ , y₁) ≡ ( 0 ,2)

For point B( x₂ , y₂)

Put y= 0 in the given equation we get

0= 4x+2

∴ point B( x₂ , y₂)  ≡

Therefore,

The two points for the line 2x - 4y = 20 are

point A( x₁ , y₁) ≡ ( 0 ,-5)

point B( x₂ , y₂) ≡ (2 , 0)

Similarly,

For y = -x + 7

Put x = 0 in the given equation we get

y=-(0) + 7 =7

y=7

∴ y = 7

∴ point C( x₁ , y₁) ≡ ( 0 , 7)

For point D( x₂ , y₂)

Put y= 0 in the given equation we get

0= -x+7

∴ x = 7

∴ point D( x₂ , y₂)  ≡ ( 7 , 0 )

For line , y = 4x + 2 ......Red color Line on Graph

point A( x₁ , y₁) ≡ ( 0 ,2)       .....Green color point on graph

point B( x₂ , y₂) ≡ ..........Blue color point on graph

For line , y = -x + 7 ............Purple color Line on Graph

point C( x₁ , y₁) ≡ ( 0 , 7 )  .....Black color point on graph

point D( x₂ , y₂) ≡ ( 7 , 0 ) ...Red color point on graph

Point of Intersection is ( 1 , 6 )  ....Orange Color

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: