Question

Graph the linear equation y=−6x−4.(1 point)
Responses

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 4 right parenthesis, and left parenthesis 1 comma negative 10 right parenthesis.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.

Answer 1

To graph the linear equation \( y = -6x - 4 \), we can identify a couple of key characteristics of the equation:

1. **Slope (m)**: The slope of the line is -6, which means that for every 1 unit increase in \( x \), \( y \) decreases by 6 units.

2. **Y-intercept (b)**: The y-intercept is -4, which means the line crosses the y-axis at the point (0, -4).

Based on the equation, we can plot the following points:

- **Point 1**: The y-intercept (0, -4).
- **Point 2**: To find another point, we can choose \( x = 1 \):
\[
y = -6(1) - 4 = -6 - 4 = -10
\]
This gives us the point (1, -10).

Now we can plot these points on the coordinate plane:

- (0, -4), which is on the y-axis,
- (1, -10), which is one unit to the right and six units down from (0, -4).

Given the slope, we can confirm the line will move downward as you move to the right, consistent with a negative slope.

Among the provided illustrations, the response that correctly represents the plot of the points (0, -4) and (1, -10) with a downward sloping line is the first option:

- **First response illustration**: A line joining the points (0, -4) and (1, -10) with arrows on both ends indicates that the line continues infinitely in both directions.

Thus, the correct graph of the linear equation \( y = -6x - 4 \) corresponds to the first description.