Question

graph the line.
y = -5x + 1

Explanation:

Step1: Identify slope and y-intercept

The equation \( y = -5x + 1 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-5 \) and \( b = 1 \). So the line crosses the y - axis at \( (0,1) \).

Step2: Plot the y - intercept

On the coordinate plane, find the point \( (0,1) \) (since the y - intercept is when \( x = 0 \)) and mark it.

Step3: Use the slope to find another point

The slope \( m=-5=\frac{- 5}{1}\). From the point \( (0,1) \), move down 5 units (because the numerator of the slope is - 5, which represents a change in \( y \)) and then move 1 unit to the right (because the denominator of the slope is 1, which represents a change in \( x \)). This gives the point \( (1,1 - 5)=(1,-4) \). Alternatively, we can move up 5 units and left 1 unit from \( (0,1) \) to get \( (-1,1 + 5)=(-1,6) \).

Step4: Draw the line

Draw a straight line through the points that we have plotted (e.g., \( (0,1) \) and \( (1,-4) \) or \( (0,1) \) and \( (-1,6) \)).

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y=-5x + 1 \) with the y - intercept at \( (0,1) \) and passing through other points found using the slope. If we were to describe the key points, the line passes through \( (0,1) \) and \( (1,-4) \) (or other points calculated from the slope).)

Answer:

The line \( y = - 5x+1 \) is graphed by plotting the y - intercept \( (0,1) \) and then using the slope \( - 5 \) to find another point (e.g., \( (1,-4) \)) and drawing a straight line through these points.