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The graph of the equation y=12x+2 is displayed. Which equations would intersect the orange line at the y-intercept? Select the three that apply.(3 points)Responsesy−2=4xy minus 2 is equal to 4 xy=3x+5y is equal to 3 x plus 5y=2x−2y is equal to 2 x minus 23y=−9x−63 y is equal to negative 9 x minus 6y=2−73xy is equal to 2 minus 7 thirds xy=7x+2

1 answer

To find which equations intersect the orange line \( y = 12x + 2 \) at the y-intercept, we need to determine the y-coordinate of the y-intercept of the orange line.

The y-intercept occurs when \( x = 0 \):

\[ y = 12(0) + 2 = 2 \]

So, the orange line intersects the y-axis at the point \( (0, 2) \). We need to find the equations from the given list that also pass through the point \( (0, 2) \).

Let's analyze each equation:

  1. Equation: \( y - 2 = 4x \)
    At \( x = 0 \),
    \( y - 2 = 4(0) \)
    \( y - 2 = 0 \)
    \( y = 2 \) (Intersects at \( (0, 2) \))

  2. Equation: \( y = 3x + 5 \)
    At \( x = 0 \),
    \( y = 3(0) + 5 \)
    \( y = 5 \) (Does not intersect at \( (0, 2) \))

  3. Equation: \( y = 2x - 2 \)
    At \( x = 0 \),
    \( y = 2(0) - 2 \)
    \( y = -2 \) (Does not intersect at \( (0, 2) \))

  4. Equation: \( 3y = -9x - 6 \)
    This can be rearranged to \( y = -3x - 2 \).
    At \( x = 0 \),
    \( y = -3(0) - 2 \)
    \( y = -2 \) (Does not intersect at \( (0, 2) \))

  5. Equation: \( y = 2 - \frac{7}{3}x \)
    At \( x = 0 \),
    \( y = 2 - \frac{7}{3}(0) \)
    \( y = 2 \) (Intersects at \( (0, 2) \))

  6. Equation: \( y = 7x + 2 \)
    At \( x = 0 \),
    \( y = 7(0) + 2 \)
    \( y = 2 \) (Intersects at \( (0, 2) \))

Summary:

The equations that intersect the orange line at the y-intercept \( (0, 2) \) are:

  1. \( y - 2 = 4x \)
  2. \( y = 2 - \frac{7}{3}x \)
  3. \( y = 7x + 2 \)

So, the three equations that apply are:

  • \( y - 2 = 4x \)
  • \( y = 2 - \frac{7}{3}x \)
  • \( y = 7x + 2 \)