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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 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.

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.

1 answer

To gather the correct graph for the linear equation \( y = 23x - 1 \), we can identify two key features of the equation:

  1. Slope: The coefficient of \( x \) (which is 23) indicates a steep incline. For every 1 unit increase in \( x \), \( y \) increases by 23 units.
  2. Y-intercept: When \( x = 0 \), \( y = -1 \). This is the point where the line crosses the y-axis.

Let's calculate a few points using the equation:

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

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

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

Based on these calculations, we can plot (0, -1) and (1, 22) on the graph. Since the slope is very steep, if the plotted points on the graph include (0, -1) and another point close to the coordinates calculated for \( x = 1 \) (or, calculating more points if necessary), it should yield a steep upward line.

Among the options you provided, the correct illustration should show:

  • A point at (0, -1)
  • Another plotted point that is consistent with a steep slope.

Given the options:

  • If one of the given lines passes through the point (0, -1) and aligns with a steep incline, that would be the correct representation of the equation.

Make sure to compare with the calculated values. Since none of the plotted point combinations in the visual options specify (1, 22) which is very high, check points close to the y-intercept to verify the steeper nature of the line described by \( y = 23x - 1 \). However, the correct representation in a feasible range will likely show the quality of that steep slope, perhaps lower end coordinates near (0, -1). If you find points approximate to these, that will be your answer.