Final answer:
To graph the equation -3x-2y=2, solve for y to find points and then plot them on a graph. Three points to plot could be (0, -1), (2, -4), and (-2, 1). The procedure is similar to graphing any linear equation, like y = 9 + 3x, which has a slope of 3 and y-intercept of 9.
Step-by-step explanation:
To graph the linear equation -3x-2y=2, let's find three points that satisfy the equation. First, we need to isolate y by adding 3x to both sides and then dividing by -2, which gives us y = -(3x+2)/2.
Let's pick three values for x and solve for y to get our points:
- Let x = 0: y = -(3(0)+2)/2 = -1. So, one point is (0, -1).
- Let x = 2: y = -(3(2)+2)/2 = -4. Another point is (2, -4).
- Let x = -2: y = -(3(-2)+2)/2 = 1. The third point is (-2, 1).
Now, we can plot these points on a graph and draw a line through them, representing the equation.
To contrast, let's briefly discuss the equation y = 9 + 3x, where the slope (m) is 3 and the y-intercept (b) is 9. The slope indicates a rise of 3 units on the vertical axis for every increase of 1 unit on the horizontal axis, which is evident in Figure A1. The y-intercept is the point where the line crosses the y-axis, in this case at y = 9.