Answer to Question #296724 in Algebra for austyn

Question

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

​(−2​,−2​) and ​(−4​,−3​)

Answer 1

Explanations & Calculations

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

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

• Now, try removing the unknown "$\small b$ " by performing $\small (1)-(2)$ and obtain a value for "$a$ ".
• Then substitute that value of "\\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.