Graph the linear equation

Question

y=2/3x−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 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.

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 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.

GPT-4o mini · Answer

To graph the linear equation $y = \frac{2}{3}x - 1$, we can follow these steps: 1. **Identify the y-intercept:** This equation is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, the y-intercept ($b$) is -1. This means the line crosses the y-axis at the point (0, -1). 2. **Identify the slope:** The slope ($m$) is $\frac{2}{3}$. This means that for every increase of 3 units in the x-direction, the value of y increases by 2 units. 3. **Plot the y-intercept (0, -1):** Start by plotting the point (0, -1) on the coordinate plane. 4. **Use the slope to find another point:** From (0, -1), move 3 units to the right (positive x-direction) and 2 units up (positive y-direction) to get to the point (3, 1). Plot this point as well. 5. **Draw the line:** Draw a straight line through the two points (0, -1) and (3, 1), extending the line in both directions. Now, let's check the plotted points mentioned in the responses: - **Response 1:** Points (0, -1) and (3, 1) are correctly plotted. - **Response 2:** Points (-2, -2) and (0, 1) do not match the equation. - **Response 3:** Points (0, -4) and (1, 2) do not match the equation. - **Response 4:** Points (0, -2) and (1, -9) do not match the equation. The correct answer is Response 1, where the line passes through the points (0, -1) and (3, 1).