Question

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

Answer 1

Answer:

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

$y=4x+2$

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

$x=\dfrac{-1}{2}$

∴ point B( x₂ , y₂)  ≡ $(\dfrac{-1}{2},0)$

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) ≡ $(\dfrac{-1}{2},0)$ ..........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