Question

watch out for that intersection practice problems(online)
use the desmos graphing calculator to determine which two equations have (-6, -2) as their solution.
i. $y = -x - 8$
ii. $y = \frac{2}{3}x + 2$
iii. $y = \frac{1}{2}x - 1$

Explanation:

Step1: Check Equation I

Substitute \( x = -6 \) and \( y = -2 \) into \( y = -x - 8 \).
Right - hand side: \( -(-6)-8=6 - 8=-2 \), which is equal to the left - hand side \( y=-2 \). So \((-6,-2)\) is a solution of Equation I.

Step2: Check Equation II

Substitute \( x = -6 \) and \( y = -2 \) into \( y=\frac{2}{3}x + 2 \).
Right - hand side: \(\frac{2}{3}\times(-6)+2=-4 + 2=-2\), which is equal to the left - hand side \( y = -2 \). So \((-6,-2)\) is a solution of Equation II.

Step3: Check Equation III

Substitute \( x=-6 \) and \( y = -2 \) into \( y=\frac{1}{2}x-1 \).
Right - hand side: \(\frac{1}{2}\times(-6)-1=-3 - 1=-4
eq - 2\). So \((-6,-2)\) is not a solution of Equation III.

Answer:

The two equations are \( y=-x - 8 \) (Equation I) and \( y=\frac{2}{3}x + 2 \) (Equation II)