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Find the x-intercept by setting f(x) = 0.

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Here are the intercepts for each function:

  1. f(x)=x−4f(x) = x - 4
  1. Find the x-intercept by setting f(x)=0f(x) = 0.

    $$
    0 = x - 4
    $$
    $$
    x = 4
    $$
    The x-intercept is $(4, 0)$.
    
  2. Find the y-intercept by setting x=0x = 0.

    $$
    f(0) = 0 - 4
    $$
    $$
    f(0) = -4
    $$
    The y-intercept is $(0, -4)$.  
    The intercepts are $\boxed{x\text{-intercept: } (4, 0), y\text{-intercept: } (0, -4)}$.
    

    2. g(x)=4x+8g(x) = 4x + 8

  3. Find the x-intercept by setting g(x)=0g(x) = 0.

    $$
    0 = 4x + 8
    $$
    $$
    4x = -8
    $$
    $$
    x = -2
    $$
    The x-intercept is $(-2, 0)$.
    
  4. Find the y-intercept by setting x=0x = 0.

    $$
    g(0) = 4(0) + 8
    $$
    $$
    g(0) = 8
    $$
    The y-intercept is $(0, 8)$.  
    The intercepts are $\boxed{x\text{-intercept: } (-2, 0), y\text{-intercept: } (0, 8)}$.
    

    3. y=35x−3y = \frac{3}{5}x - 3

  5. Find the x-intercept by setting y=0y = 0.

    $$
    0 = \frac{3}{5}x - 3
    $$
    $$
    \frac{3}{5}x = 3
    $$
    $$
    3x = 15
    $$
    $$
    x = 5
    $$
    The x-intercept is $(5, 0)$.
    
  6. Find the y-intercept by setting x=0x = 0.

    $$
    y = \frac{3}{5}(0) - 3
    $$
    $$
    y = -3
    $$
    The y-intercept is $(0, -3)$.  
    The intercepts are $\boxed{x\text{-intercept: } (5, 0), y\text{-intercept: } (0, -3)}$.
    

    4. x=2x = 2

  7. This is a vertical line.

    The x-intercept is where the line crosses the x-axis.  
    The x-intercept is $(2, 0)$.
    
  8. The y-intercept is where the line crosses the y-axis.

    Since $x=2$ is a vertical line, it is parallel to the y-axis and never crosses it.  
    There is no y-intercept.  
    The intercepts are $\boxed{x\text{-intercept: } (2, 0), \text{no y-intercept}}$.
    

    5. y=−3y = -3

  9. This is a horizontal line.

    The x-intercept is where the line crosses the x-axis.  
    Since $y=-3$ is a horizontal line, it is parallel to the x-axis and never crosses it.  
    There is no x-intercept.
    
  10. The y-intercept is where the line crosses the y-axis.

    The y-intercept is $(0, -3)$.  
    The intercepts are $\boxed{\text{no x-intercept}, y\text{-intercept: } (0, -3)}$.
    

    6. 5x−2y=105x - 2y = 10

  11. Find the x-intercept by setting y=0y = 0.

    $$
    5x - 2(0) = 10
    $$
    $$
    5x = 10
    $$
    $$
    x = 2
    $$
    The x-intercept is $(2, 0)$.
    
  12. Find the y-intercept by setting x=0x = 0.

    $$
    5(0) - 2y = 10
    $$
    $$
    -2y = 10
    $$
    $$
    y = -5
    $$
    The y-intercept is $(0, -5)$.  
    The intercepts are $\boxed{x\text{-intercept: } (2, 0), y\text{-intercept: } (0, -5)}$.
    
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