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Graph the linear equation

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 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.

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.

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 linear equation \( y = 23x - 1 \), we can follow a few steps:

  1. Identify the slope and y-intercept:

    • The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
    • Here, the slope \( m = 23 \) and the y-intercept \( b = -1 \).

  2. Plot the y-intercept:

    • Start by plotting the point (0, -1) on the y-axis.

  3. Use the slope to find another point:

    • Since the slope is \( 23 \), this means that for each increase of 1 in \( x \), \( y \) increases by 23.
    • From (0, -1), if we increase \( x \) by 1, \( y \) becomes \( 23(1) - 1 = 22 \). So the point (1, 22) can be plotted.

  4. Draw the line:

    • Once two points (0, -1) and (1, 22) are plotted, draw a line through these points extending in both directions.

However, based on the provided descriptions of the graphs, none of the options seem to fit precisely with the equation \( y = 23x - 1 \). The points described for each option do not reflect the very steep slope of 23 or the correct y-intercept of -1.

If you're looking for the most accurate representation for \( y = 23x - 1 \), you would expect:

  • The line will be very steep because of the high slope.
  • The points on the line would go significantly higher in the y-direction as x increases due to the steep slope.

Make sure to plot the line correctly on a graph if working with graph paper or graphing software, and confirm the range of your axes can accommodate the steepness of the line.