Question

1. what is the graph of $y = -4x - 1$?

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 \( b = - 1 \).

Step2: Plot the y-intercept

The y - intercept \( b=-1 \) means the line crosses the y - axis at the point \( (0,-1) \).

Step3: Use the slope to find another point

The slope \( m=-4=\frac{-4}{1} \). From the point \( (0,-1) \), we can move down 4 units (because the numerator of the slope is - 4, which represents a change in y) and then 1 unit to the right (because the denominator of the slope is 1, which represents a change in x). So we get the point \( (0 + 1,-1-4)=(1,-5) \). We can also move up 4 units and 1 unit to the left: \( (0 - 1,-1 + 4)=(-1,3) \).

Step4: Draw the line

Draw a straight line through the points we found (e.g., \( (0,-1) \) and \( (1,-5) \) or \( (0,-1) \) and \( (-1,3) \)) on the coordinate grid. The line should have a negative slope (going down from left to right) with a steep slope (since the absolute value of the slope \( |-4| = 4 \) is large) and cross the y - axis at \( (0,-1) \).

Answer:

To graph \( y=-4x - 1 \), plot the y - intercept at \( (0,-1) \). Then, using the slope \( - 4 \) (rise - 4, run 1 or rise 4, run - 1), find another point and draw a straight line through the points. The graph is a straight line with a slope of - 4 and a y - intercept of - 1. If we were to describe its appearance on the given grid, it would pass through \( (0,-1) \) and, for example, \( (1,-5) \) (or other points calculated from the slope), with a steep, negative - sloped line.