Question

graph $y = -7x - 1$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = -7x - 1 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-7 \) and \( b = - 1 \).

Step2: Plot the y-intercept

The y - intercept \( b=-1 \) means the line crosses the y - axis at the point \( (0,-1) \). So we plot the point \( (0, - 1) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=-7=\frac{-7}{1} \). The slope is the ratio of the change in \( y \) to the change in \( x \) (\( \frac{\Delta y}{\Delta x} \)). Starting from the point \( (0,-1) \), we move down 7 units (because the numerator of the slope is - 7, which means a decrease in \( y \)) and then 1 unit to the right (because the denominator of the slope is 1, which means an increase in \( x \)). So from \( (0,-1) \), moving down 7 units gives \( y=-1 - 7=-8 \) and moving right 1 unit gives \( x = 0+1 = 1 \). So we get the point \( (1,-8) \). We can also move up 7 units and left 1 unit from \( (0,-1) \): \( y=-1 + 7 = 6 \) and \( x=0 - 1=-1 \), giving the point \( (-1,6) \).

Step4: Draw the line

Now that we have two points \( (0,-1) \) and \( (1,-8) \) (or \( (-1,6) \) and \( (0,-1) \)), we can draw a straight line passing through these two points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \( y=-7x - 1 \) passing through the points we found, like \( (0,-1) \) and \( (1,-8) \) or other points determined by the slope from the y - intercept.)

Answer:

The graph of \( y=-7x - 1 \) is a straight line passing through the point \( (0,-1) \) with a slope of - 7. For example, it also passes through \( (1,-8) \) (or \( (-1,6) \)) and the line is drawn connecting these (and other) points on the coordinate plane.