Question

graph the line,
y = 2x - 6

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 2x - 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 2 \) and \( b=-6 \). So the line crosses the y - axis at the point \( (0,-6) \).

Step2: 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 \( x = 1 \) (right 1 unit), then \( y=-6 + 2=-4 \). So we get the point \( (1,-4) \). We can also find a point by setting \( y = 0 \) to find the x - intercept:
Set \( y = 0 \) in \( y=2x - 6 \), then \( 0=2x-6 \).

Step3: Solve for x (x - intercept)

Add 6 to both sides of the equation \( 0 = 2x-6 \): \( 6=2x \).
Divide both sides by 2: \( x=\frac{6}{2}=3 \). So the x - intercept is at the point \( (3,0) \).

Step4: Plot the points and draw the line

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

(Note: To graph the line, you can use the two - point form. Using the y - intercept \( (0,-6) \) and the x - intercept \( (3,0) \) is a simple way. Plot these two points and then draw a line connecting them. The slope of 2 means the line will be rising from left to right.)

Answer:

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

1. Plot the y - intercept: The point \( (0,-6) \) (since when \( x = 0 \), \( y=-6 \)).
2. Plot the x - intercept: Solve \( 0 = 2x-6\Rightarrow x = 3 \), so the point \( (3,0) \).
3. Draw a straight line through the points \( (0,-6) \) and \( (3,0) \) (or use other points found using the slope). The line should have a slope of 2 (rising 2 units for every 1 unit to the right) and pass through these points.