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Graph the linear equation

y=23x−1
.

(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 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 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.

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.

1 answer

To graph the equation \(y = 23x - 1\), we can start by finding some key points by substituting values for \(x\).

  1. Finding Points:

    • When \(x = 0\): \[ y = 23(0) - 1 = -1 \quad \text{(Point: (0, -1))} \]
    • When \(x = 1\): \[ y = 23(1) - 1 = 22 \quad \text{(Point: (1, 22))} \]
    • When \(x = -1\): \[ y = 23(-1) - 1 = -24 \quad \text{(Point: (-1, -24))} \]

  2. Plotting Points: You can plot the points you've calculated: (0, -1), (1, 22), and (-1, -24) on the coordinate plane.

  3. Graphing the Line: After plotting these points, draw a straight line through them and extend the line with arrows at both ends.

From the options provided in the question, the plotted points and line need to represent the equation \(y = 23x - 1\) accurately. The correct graph will have a very steep slope since the coefficient of \(x\) is 23, meaning that as \(x\) increases, \(y\) will increase significantly.

Given the options, the correct graph should reflect these calculations and match the resulting points you find from \(y = 23x - 1\). Based on the descriptions provided, you would need the graph that passes through (0, -1) and has a steep incline corresponding to the slope of 23.