G1a
Practice - Points (x,y)
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. You have a line representing the equation 3x - 2y = 6. The line passes through which of the following coordinates? a) (3, 2), b) (2,3), c) (4,3), or d) (3,4) ?
2. Draw an x,y graph. Place the following points on the graph: (-5,2), (4,-1), and (-2,-3).
3. Use the equation y = 3x + 3. When x = 0, what is y? When x = 2, what is y? When x = -2, what is y? What are the coordinates of these three points?
4. A line with equation y = 3 - 2x passes through which y-values at x=0, x=2, x=-2, and x=4?
5. A point is located at (-3,5). Which of the following equations would pass through this point? a) 3x + 2y = 5, b) y = 4x -1, c) y = 4x +2, or d) 3x - 3y = 6.
6. A rectangle is drawn on an x,y plot. Three of the corners are at the points (-1,-2), (-1,4), and (2,-2). What are the coordinates of the other corner?
ANSWERS
1. (4,3), because (3 x 4) - (2 x 3) = 12 - 6 = 6. None of other coordinates satisfy the equation.
2. For each x-coordinate, count the number of horizontal spaces, plus or minus. For each y-coordinate, count the number of vertical spaces, plus or minus.
3. When x = 0, y = 3. When x = 2, y = 6 + 3 = 9. When x = -2, y = -6 + 3 = 3. The three coordinates are (0,3), (2,9) and (-2,3).
4. At x=0, y = 3. (This is the y-intercept.) At x = 2, y = -1. At x = -2, y = 7. At x = 4, y = -5.
5. You have to try each of the equations. For equation a), -9 + 10 is not equal to 5. For equation b) 5 is not equal to -12 -1. For equation c), 5 is not equal to -12 +2. For equation d) -9 + 15 equals 6, so this is the correct answer.
6. You can draw the rectangle to get the answer. Alternatively, you start by focusing on the x-coordinates. You can see that the bottom of the rectangle is on the horizontal line x = -1 and that the top of the rectangle is on the horizontal line x = 2. You already have two points on x = -1, so the x-coordinate of the missing point must be the other one, which is x = 2. Similarly, you can look at the y-coordinates and see that one side of the rectangle is on the vertical line y = -2 and that the other side is on the vertical line y = 4. You already have two points on y = -2, so the y-coordinate of the missing point must be y = 4. So the coordinates of the missing point must be (2,4).