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Fill in the blanks to form an equation that passes through the point (3, 2) and creates a system of equations with the line below that has no solutions.

Fill In The Blanks To Form An Equation That Passes Through The Point 3 2 And Creates A System Of Equations With The Line Below That Has No Solutions class=

Sagot :

The linear function that passes through the point (3, 2) and creates a system of equations with the line below that has no solutions is given by:

[tex]y = -2x + 7[/tex]

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

In this problem, it creates a system without solutions with the equation:

[tex]10x + 5y = 15[/tex]

[tex]5y = 15 - 10x[/tex]

[tex]y = -2x + 3[/tex]

That is, it has the same slope of m = -2, then:

[tex]y = -2x + b[/tex]

Since it passes through the point (3,2), we have that:

[tex]3 = -2 \times 2 + b[/tex]

[tex]b = 7[/tex]

Hence, the equation is:

[tex]y = -2x + 7[/tex]

More can be learned about linear functions at https://brainly.com/question/24808124

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