Check Your Skills Answer Key

  2. 1. (2, −1): E
    2. (−1.5, −3): C
    3. (−1, 2): B
    4. (3, 2): D
    5. (2, 3): A

  		1.  x = 6

  2. y     = –2
  		3. x = 0 is the y-axis.
    1. (1, −2) is in Quadrant IV
    2. (−4.6, 7) is in Quadrant II
    3. (−1, −2.5) is in Quadrant III
    4. (3, 3) is in Quadrant I
    1. x < 0, y > 0 indicates Quadrant II
    2. x < 0, y < 0 indicates Quadrant III
    3. y > 0 indicates Quadrants I and II
    4. x < 0 indicates Quadrants II and III

  1. The point on the line with x = −3 has a y-coordinate of −4.

  1. False

    The relationship is y = 2x + 1, and the point you are testing is (9, 21). So plug in 9 for x and see what you get: y = 2(9) + 1 = 19. The point (9, 21) does not lie on the line.

  2. True

    The relationship is y = x2 − 2, and the point you are testing is (4, 14). So plug in 4 for x and see what you get: y = (4)2 − 2 = 14. The point (4, 14) lies on the curve.

  1. Slope is 3, y-intercept is 4

    The equation y = 3x + 4 is already in y = mx + b form, so you can directly find the slope and y-intercept. The slope is 3, and the y-intercept is 4.

  2. Slope is 2.5, y-intercept is −6

    To find the slope and y-intercept of a line, you need the equation to be in y = mx + b form. You need to divide the original equation by 2 to make that happen. So 2y = 5x − 12 becomes y = 2.5x − 6. So the slope is 2.5 (or 5/2) and the y-intercept is −6.

  1. Slope is 2, y-intercept is −4

    y     = 2x − 4
    slope = 2
               y-intercept = −4
  1. x-intercept is 8, y-intercept is −4

    The line is drawn on the coordinate plane shown here, but you can also answer this question using algebra.

    To determine the x-intercept, set y equal to 0, then solve for x:

    x − 2y = 8

    y = 0

    x − 0 = 8

    x = 8

    To determine the y-intercept, set x equal to 0, then solve for y:

    x − 2y = 8

    x = 0

    0 − 2y = 8

    −2y = 8

    y = −4

  1. 13

    The illustration shows the two points. A right triangle has been constructed by finding a point directly below (3, 8) and directly to the right of (−2, −4). This right triangle has legs of 5 (the change from −2 to 3) and 12 (the change from −4 to 8). You can plug those values into the Pythagorean theorem and solve for the hypotenuse:

    Alternatively, you could recognize the common Pythagorean triple 5–12–13.