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Ludmilka [50]
3 years ago
15

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

Mathematics
1 answer:
Elza [17]3 years ago
6 0

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

Download pdf
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Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
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As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
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Δ<u />>0 so the equation got 2 real solutions:
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3 is an integer number, so it's rational.
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