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lions [1.4K]
2 years ago
11

F(-4)=8 and f(-1)=4 write the linear equation

Mathematics
1 answer:
kobusy [5.1K]2 years ago
7 0

f(-4)=8\to(-4,\ 8)\\\\f(-1)=4\to(-1,\ 4)

The point-slope formula of a line:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{4-8}{-1-(-4)}=\dfrac{-4}{3}=-\dfrac{4}{3}\\\\y-8=-\dfrac{4}{3}(x-(-4))\\\\y-8=-\dfrac{4}{3}x-\dfrac{16}{3}\ \ \ \ |+8\\\\y=-\dfrac{4}{3}x-\dfrac{16}{3}+\dfrac{24}{3}\\\\y=-\dfrac{4}{3}x+\dfrac{8}{3}\ \ \ |\cdot3\\\\3y=-4x+8\ \ \ |+4x\\\\4x+3y=8

The slope-intercept form: y=-\dfrac{4}{3}x+\dfrac{8}{3}

The standard form: 4x+3y=8


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Number of solutions: no roots

Type of solution: Not Real

Step-by-step explanation:

We need to identify the number of solutions and their types using the discriminant.

We are given: 40x=10x^2+41\\

Rearranging:

40x-10x^2-41=0\\10x^2-40x+41=0

Discriminant can be found by: b^2-4ac

where b=-40, a=10 and c=41

Putting values:

b^2-4ac\\=(-40)^2-4(10)(41)\\=1600-1640\\=-40\\

So, Discriminant is -40

If the discriminant is less than zero i.e -40 then there are no real roots.

So, Number of solutions: no roots

Type of solution: Not Real

Keywords: discriminant

Learn more about discriminant at:

  • brainly.com/question/8196933
  • brainly.com/question/9328925
  • brainly.com/question/9184197

#learnwithBrainly

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