Question

3 y = -2x + 1

Explanation:

To graph the linear equation \( y = -2x + 1 \), we can use the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step 1: Identify the y - intercept

In the equation \( y=-2x + 1 \), the y - intercept \( b = 1 \). This means the line crosses the y - axis at the point \( (0,1) \). So we plot the point \( (0,1) \) on the coordinate plane.

Step 2: Identify the slope

The slope \( m=-2 \). We can write the slope as a fraction \( m=\frac{-2}{1}=\frac{\text{rise}}{\text{run}} \). The "rise" is the change in \( y \) and the "run" is the change in \( x \). A slope of \( - 2\) (or \( \frac{-2}{1}\)) means that for every 1 unit we move to the right (increase in \( x \) by 1), we move down 2 units (decrease in \( y \) by 2).

Starting from the y - intercept \( (0,1) \):

• If we move 1 unit to the right (run = 1) to \( x = 1 \), then we move down 2 units (rise=- 2) from \( y = 1 \). So \( y=1-2=-1 \). This gives us the point \( (1, - 1) \).
• We can also go in the opposite direction. If we move 1 unit to the left (run=-1) from \( (0,1) \), we move up 2 units (rise = 2) because \( \frac{\text{rise}}{\text{run}}=\frac{2}{-1}=-2 \). So \( x = 0-1=-1 \) and \( y=1 + 2=3 \), giving us the point \( (-1,3) \).

Step 3: Draw the line

Once we have at least two points (e.g., \( (0,1) \), \( (1,-1) \), \( (-1,3) \)), we can draw a straight line passing through these points. This line represents the graph of the equation \( y=-2x + 1 \).

If we want to find more points, we can also create a table of values:

\( x \)	\( y=-2x + 1 \)
- 1	\( y=-2\times(-1)+1=2 + 1=3 \)
0	\( y=-2\times0+1=1 \)
1	\( y=-2\times1+1=-2 + 1=-1 \)
2	\( y=-2\times2+1=-4 + 1=-3 \)

We can plot these points \( (-2,5) \), \( (-1,3) \), \( (0,1) \), \( (1,-1) \), \( (2,-3) \) and draw a straight line through them.

Answer:

To graph the linear equation \( y = -2x + 1 \), we can use the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step 1: Identify the y - intercept

In the equation \( y=-2x + 1 \), the y - intercept \( b = 1 \). This means the line crosses the y - axis at the point \( (0,1) \). So we plot the point \( (0,1) \) on the coordinate plane.

Step 2: Identify the slope

The slope \( m=-2 \). We can write the slope as a fraction \( m=\frac{-2}{1}=\frac{\text{rise}}{\text{run}} \). The "rise" is the change in \( y \) and the "run" is the change in \( x \). A slope of \( - 2\) (or \( \frac{-2}{1}\)) means that for every 1 unit we move to the right (increase in \( x \) by 1), we move down 2 units (decrease in \( y \) by 2).

Starting from the y - intercept \( (0,1) \):

• If we move 1 unit to the right (run = 1) to \( x = 1 \), then we move down 2 units (rise=- 2) from \( y = 1 \). So \( y=1-2=-1 \). This gives us the point \( (1, - 1) \).
• We can also go in the opposite direction. If we move 1 unit to the left (run=-1) from \( (0,1) \), we move up 2 units (rise = 2) because \( \frac{\text{rise}}{\text{run}}=\frac{2}{-1}=-2 \). So \( x = 0-1=-1 \) and \( y=1 + 2=3 \), giving us the point \( (-1,3) \).

Step 3: Draw the line

Once we have at least two points (e.g., \( (0,1) \), \( (1,-1) \), \( (-1,3) \)), we can draw a straight line passing through these points. This line represents the graph of the equation \( y=-2x + 1 \).

If we want to find more points, we can also create a table of values:

\( x \)	\( y=-2x + 1 \)
- 1	\( y=-2\times(-1)+1=2 + 1=3 \)
0	\( y=-2\times0+1=1 \)
1	\( y=-2\times1+1=-2 + 1=-1 \)
2	\( y=-2\times2+1=-4 + 1=-3 \)

We can plot these points \( (-2,5) \), \( (-1,3) \), \( (0,1) \), \( (1,-1) \), \( (2,-3) \) and draw a straight line through them.