Question #296724

Find an equation of the line passing through the given points. Use function notation to write the equation.

​(−2​,−2​) and ​(−4​,−3​)


1
Expert's answer
2022-02-14T17:18:27-0500

Explanations & Calculations


  • The function notation of a line is given by y=ax+b\small y=ax+b\\
  • Now use the 2 sets of data to form a pair of simultaneous equations and solve for each unknown.

(2,2):2=a(2)+b2=2a+b(1)(4,3):3=a(4)+b3=4a+b(2)\qquad\qquad \begin{aligned} \small (-2,-2):\qquad-2&=\small a(-2)+b\\ \small -2&=\small -2a+b\cdots\cdots(1)\\ \\ \small (-4,-3):\qquad -3&=\small a(-4)+b\\ \small -3&=\small -4a+b\cdots \cdots(2) \end{aligned}

  • Now, try removing the unknown "b\small b " by performing (1)(2)\small (1)-(2) and obtain a value for "aa ".
  • Then substitute that value of "a"\small "a" in either of the two equations (in (1) for example) and calculate the value of "b".


  • The write the function with those found values.

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