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Find the gradient y-intercepts. a) y=3x−2 b) y=2x+4=0 c) x+y=0 d) y=-3x+6 e) x−y=0 f) 3x+y=2 g) x−y=2 h) y-(2x-2)

Mathematics

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Step-by-step solution

16 steps

Here are the solutions for finding the gradient and y-intercept for each equation. The general form of a linear equation is y=mx+cy = mx + c, where mm is the gradient and cc is the y-intercept.

Part a· 2 steps

y=3x−2y = 3x - 2

  1. The equation is already in the form y=mx+cy = mx + c.

  2. Identify the gradient and y-intercept.

    The gradient is m=3m = 3.
    The y-intercept is c=−2c = -2.
    Gradient: 3\boxed{\textbf{3}}
    Y-intercept: -2\boxed{\textbf{-2}}

Part b· 2 steps

y=2x+4=0y = 2x + 4 = 0

Assuming the intended equation is y=2x+4y = 2x + 4.

  1. The equation is already in the form y=mx+cy = mx + c.

  2. Identify the gradient and y-intercept.

    The gradient is m=2m = 2.
    The y-intercept is c=4c = 4.
    Gradient: 2\boxed{\textbf{2}}
    Y-intercept: 4\boxed{\textbf{4}}

Part c· 2 steps

x+y=0x + y = 0

  1. Rearrange the equation into y=mx+cy = mx + c form.

    x+y=0x + y = 0 y=−xy = -x y=−1x+0y = -1x + 0
  2. Identify the gradient and y-intercept.

    The gradient is m=−1m = -1.
    The y-intercept is c=0c = 0.
    Gradient: -1\boxed{\textbf{-1}}
    Y-intercept: 0\boxed{\textbf{0}}

Part d· 2 steps

y=−3x+6y = -3x + 6

  1. The equation is already in the form y=mx+cy = mx + c.

  2. Identify the gradient and y-intercept.

    The gradient is m=−3m = -3.
    The y-intercept is c=6c = 6.
    Gradient: -3\boxed{\textbf{-3}}
    Y-intercept: 6\boxed{\textbf{6}}

Part e· 2 steps

x−y=0x - y = 0

  1. Rearrange the equation into y=mx+cy = mx + c form.

    x−y=0x - y = 0 x=yx = y y=xy = x y=1x+0y = 1x + 0
  2. Identify the gradient and y-intercept.

    The gradient is m=1m = 1.
    The y-intercept is c=0c = 0.
    Gradient: 1\boxed{\textbf{1}}
    Y-intercept: 0\boxed{\textbf{0}}

Part f· 2 steps

3x+y=23x + y = 2

  1. Rearrange the equation into y=mx+cy = mx + c form.

    3x+y=23x + y = 2 y=−3x+2y = -3x + 2
  2. Identify the gradient and y-intercept.

    The gradient is m=−3m = -3.
    The y-intercept is c=2c = 2.
    Gradient: -3\boxed{\textbf{-3}}
    Y-intercept: 2\boxed{\textbf{2}}

Part g· 2 steps

x−y=2x - y = 2

  1. Rearrange the equation into y=mx+cy = mx + c form.

    x−y=2x - y = 2 −y=−x+2-y = -x + 2 y=x−2y = x - 2 y=1x−2y = 1x - 2
  2. Identify the gradient and y-intercept.

    The gradient is m=1m = 1.
    The y-intercept is c=−2c = -2.
    Gradient: 1\boxed{\textbf{1}}
    Y-intercept: -2\boxed{\textbf{-2}}

Part h· 2 steps

y−(2x−2)y - (2x - 2)

Assuming the intended equation is y=2x−2y = 2x - 2.

  1. The equation is already in the form y=mx+cy = mx + c.

  2. Identify the gradient and y-intercept.

    The gradient is m=2m = 2.
    The y-intercept is c=−2c = -2.
    Gradient: 2\boxed{\textbf{2}}
    Y-intercept: -2\boxed{\textbf{-2}}

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