maddyhelps

Math 10C

Math 10C · Worksheets

Linear functions and systems

Ten questions of mixed difficulty, covering Linear functions. Print it, or work through it on screen — the answer key starts on its own page.

All worksheets

Linear functions and systems

Math 10C · maddyhelps.com

Name
Date
Score
/ 10

Circle the best answer for each question. Show your work in the space provided.

  1. The equation of a line with slope −2 through (0, 5) is

    1. a) y = 5x − 2
    2. b) y = −2x + 5
    3. c) y = 2x + 5
    4. d) y = −2x − 5

  2. A horizontal line has slope

    1. a) undefined
    2. b) 1
    3. c) −1
    4. d) 0

  3. The solution to y = x + 4 and 2x + y = 10 is

    1. a) (2, 6)
    2. b) (3, 7)
    3. c) (6, 2)
    4. d) (4, 2)

  4. A line through (1, 2) and (3, 8) has slope

    1. a) 3
    2. b) 2
    3. c) 1/3
    4. d) 6

  5. The line 2x + 3y = 12 has slope

    1. a) −3/2
    2. b) 12
    3. c) 2/3
    4. d) −2/3

  6. Slope is defined as

    1. a) run over rise
    2. b) the x-intercept
    3. c) rise over run
    4. d) the y-intercept

  7. A line perpendicular to one with slope 3/4 has slope

    1. a) −3/4
    2. b) 4/3
    3. c) −4/3
    4. d) 3/4

  8. In y = mx + b, the value of b is the

    1. a) domain
    2. b) slope
    3. c) y-intercept
    4. d) x-intercept

  9. Solving 3x + 2y = 16 and 3x − y = 1 by elimination gives

    1. a) (4, 2)
    2. b) (2, 5)
    3. c) (2, 2)
    4. d) (5, 2)

  10. The system y = 2x + 1 and y = 2x − 3 has

    1. a) one solution
    2. b) infinitely many solutions
    3. c) a solution at the origin
    4. d) no solution, because the lines are parallel

Answer key · Linear functions and systems

Math 10C · maddyhelps.com

  1. b) y = −2x + 5 — The point is on the y-axis, so it is the intercept and slope-intercept form can be written straight down. A negative slope means the line falls from left to right, which matches.
  2. d) 0 — There is no rise, so the slope is 0 ÷ run = 0. A <i>vertical</i> line is the other case: the run is zero, and dividing by zero makes its slope undefined rather than zero.
  3. a) (2, 6) — Substitute the first into the second: 2x + (x + 4) = 10, so 3x = 6 and x = 2, giving y = 6. Always substitute back into the <i>other</i> equation to check: 2(2) + 6 = 10 ✓.
  4. a) 3 — Slope = (8 − 2)/(3 − 1) = 6/2 = 3. Subtract the coordinates in the same order top and bottom; swapping one of them flips the sign.
  5. d) −2/3 — Rearrange to slope-intercept: 3y = −2x + 12, so y = −(2/3)x + 4. From general form Ax + By + C = 0 the slope is −A/B, which gives the same answer without rearranging.
  6. c) rise over run — Slope is the change in y divided by the change in x — how much the line goes up for each step across. It is a rate of change, which is why it has units in a real-world problem.
  7. c) −4/3 — Perpendicular slopes are negative reciprocals: flip the fraction and change the sign. Their product is always −1, which is a quick way to check.
  8. c) y-intercept — Setting x = 0 leaves y = b, which is where the line crosses the y-axis. And m is the slope, which is why this is called slope-intercept form — it hands you both.
  9. b) (2, 5) — Both equations start with 3x, so subtracting the second from the first removes it: 3y = 15, giving y = 5. Substituting back into 3x − y = 1 gives 3x = 6 and x = 2. Check in the <i>other</i> equation too: 3(2) + 2(5) = 16 ✓.
  10. d) no solution, because the lines are parallel — Same slope, different intercepts, so the lines never meet. Equal slopes <i>and</i> equal intercepts would be the same line and give infinitely many solutions.