Question

graph these equations:
$x - y = -2$
$x - 2y = -6$
click to select points on the graph.
10▲
y
8
6

Explanation:

Step1: Rewrite the first equation in slope - intercept form

The equation is \(x - y=-2\). We want to solve for \(y\) in terms of \(x\).
Subtract \(x\) from both sides: \(-y=-x - 2\).
Multiply both sides by \(- 1\): \(y=x + 2\).
To find two points on this line, we can use the \(x\) - intercept and \(y\) - intercept.

• For the \(y\) - intercept, set \(x = 0\): \(y=0 + 2=2\). So the point is \((0,2)\).
• For the \(x\) - intercept, set \(y = 0\): \(0=x + 2\), then \(x=-2\). So the point is \((-2,0)\).

Step2: Rewrite the second equation in slope - intercept form

The equation is \(x - 2y=-6\). We solve for \(y\) in terms of \(x\).
Subtract \(x\) from both sides: \(-2y=-x - 6\).
Divide both sides by \(-2\): \(y=\frac{1}{2}x + 3\).
To find two points on this line:

• For the \(y\) - intercept, set \(x = 0\): \(y=\frac{1}{2}(0)+3 = 3\). So the point is \((0,3)\).
• For the \(x\) - intercept, set \(y = 0\): \(0=\frac{1}{2}x+3\). Subtract 3 from both sides: \(\frac{1}{2}x=-3\). Multiply both sides by 2: \(x=-6\). So the point is \((-6,0)\).

Answer:

To graph \(y = x + 2\), plot the points \((0,2)\) and \((-2,0)\) and draw a line through them. To graph \(y=\frac{1}{2}x + 3\), plot the points \((0,3)\) and \((-6,0)\) and draw a line through them.