Graph the linear equation

Question

y=23x−1.

(1 point)
Responses

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 negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 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 upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.

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 2 right parenthesis, and left parenthesis 1 comma negative 9 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 2 right parenthesis, and left parenthesis 1 comma negative 9 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.

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 1 right parenthesis, and left parenthesis 3 comma 1 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 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
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Answer 1

To graph the linear equation \( y = 23x - 1 \), we can analyze its slope and y-intercept.

1. Y-intercept: The y-intercept occurs when \( x = 0 \). Plugging in \( x = 0 \): \[ y = 23(0) - 1 = -1 \] So the point (0, -1) is on the graph.

2. Slope: The slope is 23, which means that for every 1 unit increase in \( x \), \( y \) increases by 23 units.

3. Finding another point: Using the y-intercept (0, -1), we can find another point by increasing \( x \) by 1: \[ x = 1 \quad \Rightarrow \quad y = 23(1) - 1 = 22 \] Thus, the point (1, 22) is also on the graph.

Now, we can plot these points on a coordinate plane and draw a line through them, extending the line in both directions.

From your description, the appropriate choice that resembles this graph should have the points \((0, -1)\) and \((3, 1)\) because they are the only one that fits the model where as you increment x by a certain amount, y increases significantly due to the slope of 23.

Thus, the linear equation \( y = 23x - 1 \) is correctly represented by the graph that includes the points:

• (0, -1)
• (1, 22)

None of the points in the provided descriptions seem to accurately represent this line based on the steep slope of 23. Therefore, based on the information provided, the accurate understanding of the graph for the equation \( y=23x−1 \) may not be represented correctly in the options you've shared.