Daily Regents: Graphing a Linear Equation

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

June 2014, Question 29

29. On the set of axes below, draw the graph of the equation y = -(3/4)x + 3.
Is the point (3,2) a solution to the equation? Explain your answer based on the graph drawn.

Unlike the previous question, the graph is definitely required. You can use your graphing calculator to get the Table of Values, or you just plot the points directly using the slope and the y-intercept.

The y-intercept is 3, so the first point is (0, 3). The slope is -3/4, which means that for every four places to the right you go, the next point will be three places down. Also, for every four places to the left, the next point will be three places up.

The next point will be at (4, 0), then (8, -3). Working the other way, there are points at (-4, 6) and (-8, 9). Draw a straight line through these points. If they don't line up, you miscounted somewhere.

Don't forget to answer and explain the second part. No explanation means loss of a point.

You need three things to score two points on this question. The graph, "No" and an explanation. If you make a mistake with the graph, you will lose one point and the rest of the answer must match your graph. (That is, if by some chance, your incorrect graph goes through the point (3, 2), then you must answer "Yes" to the second question.)

Point (3, 2) is not a solution because it is not a point on the line. The points on the line are all the solutions.

If you want to use the graphing calculator, look at the images below. In Figure 1, the parentheses around the fraction are not necessary, but the are a good habit to get into if you have this version of the operating system. (Newer models will show the fractions.) You get to this screen using the Y= button.

Figure 2 shows how the graph will look. And Figure 3 shows you some of the Table of Values. (Press "2nd" and "Graph" to get this screen.) Plot the points that have whole number values.

Notice that (3, 2) is not in the Table of Values. However, you have to give your answer in reference to the line, not the table.

Any questions?

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If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.