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 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.

say if its first second third or fourth

Answer 1

To determine which graph correctly represents the linear equation \(y = 23x - 1\), we can analyze the equation to find key points.

1. Identify the y-intercept and slope:

   • The y-intercept occurs when \(x=0\): \[ y = 23(0) - 1 = -1 \] So, one point on the line is \((0, -1)\).
   • The slope of the line is 23, meaning for every unit increase in \(x\), \(y\) increases by 23.

2. Find another point using the slope:

   • If \(x = 1\): \[ y = 23(1) - 1 = 22 \] So, another point on the line is \((1, 22)\).

3. Check which graph matches these points:

   • The first option does not match because it states the line passes through \((0, -4)\) and \((1, 2)\).
   • The second option states it passes through \((-2, -2)\) and \((0, 1)\), which also does not match.
   • The third option mentions points \((0, -2)\) and \((1, -9)\), which does not match.
   • The fourth option mentions points \((0, -1)\) and \((3, 1)\), and the point \((0, -1)\) matches one of our results, but \((3, 1)\) does not match because at \(x=3\): \[ y = 23(3) - 1 = 68 \]

Given the analysis, none of the presented options seem to accurately graph the line described by the equation \(y = 23x - 1\). However, the fourth option has one correct point \((0, -1)\), but due to changes in the second point, it remains misleading.

If you were looking for a point that best matches common linear graphing properties from your descriptions, you'd likely go with the fourth one.