Practice Maths

y-intercept and Equation of a Line — Solutions

Click any answer to watch the solution video.

  1. Identify gradient and y-intercept

    1. y = 3x + 2:
    2. y = −4x + 7:
    3. y = 5x − 3:
    4. y = −x + 9:
    5. y = ½x − 6:
    6. y = 2x:
    7. y = −3:
    8. y = −2x − 8:
    9. y = ⅔x + 4:
    10. y = −¾x + 1:

  2. Write equation from gradient and y-intercept

    1. m=4, b=1:
    2. m=−2, b=5:
    3. m=3, b=0:
    4. m=−1, b=−4:
    5. m=½, b=3:
    6. m=0, b=−7:
    7. m=−5, b=2:
    8. m=⅔, b=−1:

  3. Find equation from gradient and a point

    1. m=2, (0,5):
    2. m=−3, (0,1):
    3. m=4, (1,6):
    4. m=−2, (3,4):
    5. m=1, (5,3):
    6. m=½, (2,0):
    7. m=3, (−1,2):
    8. m=−4, (2,−3):

  4. Compare pairs of lines

    1. y=2x+3 and y=2x−5:
    2. y=4x+1 and y=−4x+1:
    3. y=−x+6 and y=−x+6:
    4. y=3x−2 and y=2x−2:
    5. y=½x+4 and y=2x+4:
    6. y=5x+7 and y=5x+7:

  5. Reconstruct equation from graph description

    1. y-axis at 4, x-axis at 2:
    2. y-axis at −3, passes through (2,1):
    3. Horizontal line through (0,−5):
    4. Same y-intercept as y=3x+7, gradient −2:
    5. Through (0,0), gradient 5:
    6. Through (3,9) and (5,13):

  6. Real-world equation of a line

    1. Plumber C = 80h + 60:
      1. Call-out fee:
      2. Hourly rate:
      3. 3-hour job:
    2. Candle:
    3. Are Lines A and B the same?:
    4. Through (2,7) and (5,16):

  7. Two streaming plans

    1. (i) y-intercepts:
    2. (ii) When Plan A cheaper:
    3. (iii) Cost after 12 months:

  8. Reading a line from a graph

    1. y-intercept:
    2. Gradient using two points:
    3. Equation:
    4. Does (−2, −3) lie on the line?:

  9. Two lines on the same graph

    1. y-intercepts:
    2. Gradients:
    3. Equations:
    4. Intersection point:

  10. A line with a fractional gradient

    1. y-intercept:
    2. Gradient (rise ÷ run):
    3. Equation:
    4. Student error — why gradient is not 2:
    5. x-intercept: