Graph the linear equation y=2/3x−1 . (1 point) Responses 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. 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. 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.

Answer 1

To graph the linear equation \( y = \frac{2}{3}x - 1 \), we can identify two key points by substituting x-values into the equation.

1. Finding Points:

   • When \( x = 0 \): \[ y = \frac{2}{3}(0) - 1 = -1. \] So, the first point is \( (0, -1) \).

   • When \( x = 3 \): \[ y = \frac{2}{3}(3) - 1 = 2 - 1 = 1. \] So, the second point is \( (3, 1) \).

Now you can plot the points \( (0, -1) \) and \( (3, 1) \) on the coordinate plane.

2. Plotting the Points:

   • Plot the point \( (0, -1) \) on the y-axis.
   • Plot the point \( (3, 1) \) on the graph.

3. Drawing the Line:

   • Draw a straight line through the points you plotted. Extend the line with arrows on either end to indicate that it extends infinitely in both directions.

The description of the graph in your message does not match the equation \( y = \frac{2}{3}x - 1 \). Instead, your options appear to show different, perhaps incorrect relationships. The line \( y = \frac{2}{3}x - 1 \) should have a positive slope passing through the plotted points \( (0, -1) \) and \( (3, 1) \).

If you need further clarification or have more questions about graphing this function, feel free to ask!