Straight-line graphs Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Straight-line graphs questions. See exactly how to solve problems on y = mx + c, gradient, y-intercept, negative gradient.

y = mx + cgradienty-interceptnegative gradientgradient of 1line through origin
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
A straight line has equation y=3x+2y = 3x + 2. Write down the gradient of the line.

Worked solution

  1. Compare with y=mx+cy = mx + c

    y=3x+2y = 3x + 2

    In the form y=mx+cy = mx + c, the letter m stands for the gradient and c for the y-intercept.

  2. Identify m

    m=3m = 3

    The number multiplying x is 3, so that is the value of m.

  3. State the gradient

    gradient=3\text{gradient} = 3

    The gradient equals m, so the gradient is 3.

Answer
33
Question 2
1 markeasy
A straight line has equation y=4x+5y = 4x + 5. Write down the yy-intercept.

Worked solution

  1. Compare with y=mx+cy = mx + c

    y=4x+5y = 4x + 5

    The constant term c gives the y-intercept, where the line crosses the y-axis.

  2. Identify c

    c=5c = 5

    The number on its own (not attached to x) is 5.

  3. State the y-intercept

    y-intercept=5\text{y-intercept} = 5

    The line crosses the y-axis at a height of 55.

Answer
55
Question 3
1 markeasy
A straight line has equation y=5x−4y = 5x - 4. Write down the gradient.

Worked solution

  1. Compare with y=mx+cy = mx + c

    y=5x−4y = 5x - 4

    The gradient is the number multiplying x.

  2. Identify m

    m=5m = 5

    Here x is multiplied by 5.

  3. State the gradient

    gradient=5\text{gradient} = 5

    The gradient is 55.

Answer
55
Question 4
1 markeasy
A straight line has equation y=−2x+7y = -2x + 7. Write down the gradient.

Worked solution

  1. Compare with y=mx+cy = mx + c

    y=−2x+7y = -2x + 7

    Keep the sign that is in front of the x term.

  2. Identify m

    m=−2m = -2

    The number multiplying x is negative two.

  3. State the gradient

    gradient=−2\text{gradient} = -2

    A negative gradient means the line slopes downwards.

Answer
−2-2
Question 5
1 markeasy
A straight line has equation y=−x−3y = -x - 3. Write down the yy-intercept.

Worked solution

  1. Compare with y=mx+cy = mx + c

    y=−x−3y = -x - 3

    The constant term is the y-intercept.

  2. Identify c

    c=−3c = -3

    The number on its own is negative three.

  3. State the y-intercept

    y-intercept=−3\text{y-intercept} = -3

    The line crosses the y-axis at −3-3.

Answer
−3-3

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