Question

trazar el gráfico de la recta.
-2x + y = -6

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(-2x + y=-6\). To get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we add \(2x\) to both sides of the equation.
\(y=2x - 6\)

Step2: Find the y - intercept

The y - intercept occurs when \(x = 0\). Substitute \(x = 0\) into \(y=2x - 6\).
\(y=2(0)-6=-6\)
So the y - intercept is the point \((0,-6)\).

Step3: Find another point using the slope

The slope \(m = 2=\frac{2}{1}\), which means for every 1 unit we move to the right (increase in \(x\) by 1), we move up 2 units (increase in \(y\) by 2).
Starting from the y - intercept \((0,-6)\), if we move \(x = 1\) (increase \(x\) by 1), then \(y=-6 + 2=-4\). So another point on the line is \((1,-4)\). We can also find the x - intercept by setting \(y = 0\) in \(y=2x - 6\):
\(0=2x-6\)
Add 6 to both sides: \(2x=6\)
Divide both sides by 2: \(x = 3\). So the x - intercept is \((3,0)\).

Step4: Plot the points and draw the line

Plot the points \((0,-6)\) and \((3,0)\) (or \((1,-4)\) etc.) on the coordinate plane and then draw a straight line passing through these points.

To graph the line \(y = 2x-6\):

• Locate the y - intercept \((0,-6)\) on the y - axis.
• Locate the x - intercept \((3,0)\) on the x - axis.
• Draw a straight line connecting these two points (and extending it in both directions).

Answer:

To graph the line \(-2x + y=-6\) (or \(y = 2x-6\)):

1. Plot the y - intercept \((0,-6)\).
2. Plot the x - intercept \((3,0)\) (found by setting \(y = 0\) in \(y = 2x-6\) and solving for \(x\)).
3. Draw a straight line through \((0,-6)\) and \((3,0)\) (or use the slope \(m = 2\) to find additional points and draw the line).