Question

which of the following points lies on the graph of the equation $-x + y = 8$?
$\circ$ $(-1, 1)$
$\circ$ $(-1, 7)$
$\circ$ $(3, -5)$
$\circ$ $(8, 0)$

Explanation:

Step1: Recall the condition for a point \((x,y)\) to lie on the graph of the equation \(-x + y = 8\). A point \((x,y)\) lies on the graph if substituting \(x\) and \(y\) into the equation satisfies it, i.e., \(-x + y = 8\).

Step2: Test the first point \((-1,1)\). Substitute \(x=-1\) and \(y = 1\) into \(-x + y\): \(-(-1)+1=1 + 1=2

eq8\). So, \((-1,1)\) does not lie on the graph.

Step3: Test the second point \((-1,7)\). Substitute \(x=-1\) and \(y = 7\) into \(-x + y\): \(-(-1)+7=1 + 7 = 8\). This satisfies the equation \(-x + y = 8\).

Step4: For completeness, test the third point \((3,-5)\). Substitute \(x = 3\) and \(y=-5\) into \(-x + y\): \(-3+(-5)=-8

eq8\).

Step5: Test the fourth point \((8,0)\). Substitute \(x = 8\) and \(y = 0\) into \(-x + y\): \(-8+0=-8

eq8\).

Answer:

\((-1,7)\)