Question

1. graph this line using the slope and y-intercept:

$y = 2x - 6$

1. click to select points on the graph.

Explanation:

Step1: Identify slope and y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=2x - 6\), the slope \(m = 2=\frac{2}{1}\) and the y - intercept \(b=- 6\).

Step2: Plot the y - intercept

The y - intercept is the point where \(x = 0\). So, when \(x = 0\), \(y=-6\). We plot the point \((0,-6)\) on the graph.

Step3: Use the slope to find another point

The slope is \(\frac{\text{rise}}{\text{run}}=\frac{2}{1}\). From the point \((0,-6)\), we move up 2 units (because the rise is 2) and then 1 unit to the right (because the run is 1). This gives us the point \((0 + 1,-6+2)=(1,-4)\). We can also move down 2 units and 1 unit to the left from \((0,-6)\) to get \((- 1,-8)\), but for graphing, we can use the positive slope movement.

Step4: Draw the line

After plotting the y - intercept \((0,-6)\) and another point (e.g., \((1,-4)\) or \((3,0)\) which we can find by setting \(y = 0\) in \(y = 2x-6\) ( \(0=2x - 6\), \(2x=6\), \(x = 3\), so the x - intercept is \((3,0)\))), we draw a straight line passing through these points.

(Note: Since the question is about graphing, the key points to plot are \((0,-6)\) and \((3,0)\) (or other points found using the slope) and then drawing the line through them. )

Answer:

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

1. Plot the y - intercept at \((0,-6)\).
2. Use the slope \(m = 2\) (rise 2, run 1) to find another point (e.g., from \((0,-6)\), moving up 2 and right 1 gives \((1,-4)\), or moving up 6 and right 3 gives the x - intercept \((3,0)\)).
3. Draw a straight line through the plotted points.