How do you graph #y = -3x + 2# by plotting points?

Question

Avery Alexander · Accepted Answer

Pick out at least 2 x values, find the resulting y values, plot them on a graph, then use a straight edge to connect them.

When we plot points, we need to find at least 2 x values and the corresponding y value - and then we can use a straight edge to connect the points. With picking our x points, try to find ones that are easier to calculate. While any x value would be valid (25,657 is just as valid as 1 - they both will have a point on the line), it will be easier to calculate and graph some numbers rather than others. One of my favourites is #x=0#. So let's do that. When #x=0#: #y=-3x+2# #y=-3(0)+2# #y=2# So that's one plot point - #(0,2)# Let's do another. How about #x=1# #y=-3(1)+2# #y=-3+2# #y=-1# So that's another plot point - #(1,-1)#. If you need a table of plot points, you can pick out 2 or 3 more x values, and numbers like #2, -1, and -2# would be good candidates (and if you want to get fancy, fractions with a 3 in the denominator would be good because they would cancel against the 3 in the x-term, like this example of #x=1/3#): #y=-3(1/3)+2# #y=-1+2# #y=1# Plot them out and get: graph{-3x+2 [-5, 5, -5, 5]} (each line of the graph paper is each value 1 (so you move 5 lines to the right to get to the 5 on the x axis), and the horizontal line is x while the vertical line is y). Our first point, (0,2), can be found by going 0 spaces across on the x axis and 2 up on the y axis. Our next point, (1,-1), can be found by going 1 to the right on the x axis and 1 down on the y axis. And remember that each value on our plot of the solution is a valid answer. So if you wanted to try to plot #x=-11/245345#, you can and the point will sit on the plot very very close to our first plot point of (0,2).

Eva Abramson · Answer

undefined To graph the equation y = -3x + 2 by plotting points, you can choose a few values for x, calculate the corresponding y values using the equation, and then plot the points on a coordinate plane. For example, if you choose x = 0, you would have y = -3(0) + 2, which simplifies to y = 2. So one point on the graph would be (0, 2). Similarly, if you choose x = 1, you would have y = -3(1) + 2, which simplifies to y = -1. So another point on the graph would be (1, -1). Continuing this process for a few more values of x will give you additional points that you can plot. After plotting these points, you can draw a straight line through them to represent the graph of y = -3x + 2.