Question

graph these equations:
$x - y = -2$
$y = x - 5$
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and two buttons at the bottom: blue with $x - y = -2$ and yellow with $y = x - 5$)

Explanation:

Step1: Rewrite \(x - y = -2\) in slope - intercept form

We want to solve \(x - y=-2\) for \(y\). Subtract \(x\) from both sides: \(-y=-x - 2\). Multiply both sides by \(- 1\): \(y=x + 2\). The slope of this line is \(m = 1\) and the \(y\) - intercept is \(b = 2\). To find two points on this line, when \(x = 0\), \(y=0 + 2=2\), so the point is \((0,2)\). When \(x = 1\), \(y=1 + 2=3\), so the point is \((1,3)\).

Step2: Analyze the line \(y=x - 5\)

The equation \(y=x - 5\) is already in slope - intercept form (\(y=mx + b\)) where the slope \(m = 1\) and the \(y\) - intercept \(b=-5\). To find two points on this line, when \(x = 0\), \(y=0-5=-5\), so the point is \((0,-5)\). When \(x = 5\), \(y=5 - 5=0\), so the point is \((5,0)\).

Step3: Graph the lines

For the line \(y=x + 2\), plot the points \((0,2)\) and \((1,3)\) (or other points found) and draw a straight line through them. For the line \(y=x - 5\), plot the points \((0,-5)\) and \((5,0)\) (or other points found) and draw a straight line through them.

(Note: Since the problem is about graphing, the final answer is the graphical representation of the two lines \(y = x+2\) (from \(x - y=-2\)) and \(y=x - 5\) on the given coordinate plane. The line \(y=x + 2\) passes through \((0,2)\), \((-2,0)\) etc., and the line \(y=x - 5\) passes through \((0,-5)\), \((5,0)\) etc. )

Answer:

The line \(x - y=-2\) (or \(y=x + 2\)) has a \(y\) - intercept at \((0,2)\) and a slope of \(1\). The line \(y=x - 5\) has a \(y\) - intercept at \((0,-5)\) and a slope of \(1\). To graph them, plot the appropriate points for each line and draw the lines. The line \(y=x + 2\) passes through points like \((0,2)\), \((1,3)\), \((-1,1)\) and the line \(y=x - 5\) passes through points like \((0,-5)\), \((1,-4)\), \((5,0)\) on the given grid.