Question

graph the line.
$y = -4x + 1$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -4x + 1 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-4 \) and \( b = 1 \). So the line crosses the y - axis at \( (0,1) \).

Step2: Use the slope to find another point

The slope \( m=-4=\frac{-4}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move down 4 units (decrease in \( y \) by 4). Starting from \( (0,1) \), if we move \( x = 1 \), then \( y=1-4=-3 \). So we get the point \( (1, - 3) \). We can also move to the left: if \( x=-1 \), then \( y=-4\times(-1)+1 = 4 + 1=5 \), so we get the point \( (-1,5) \).

Step3: Plot the points and draw the line

Plot the points \( (0,1) \), \( (1,-3) \), \( (-1,5) \) on the coordinate plane and then draw a straight line through them.

(Note: Since the question is about graphing, the main steps are identifying the key points using the slope - intercept form and then plotting and connecting them. The actual graphing is a visual task, but the above steps describe how to find the points to plot.)

Answer:

To graph \( y=-4x + 1 \):

1. Plot the y - intercept at \( (0,1) \).
2. Use the slope \( m = - 4 \) to find additional points (e.g., \( (1,-3) \), \( (-1,5) \)).
3. Draw a straight line through the plotted points.