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What is the x and y intercept of y=1/3x-2, y=12-6x, and y=3x-7? Please show work!

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Answer:

y = 1/3x - 2:

  • y - intercept: - 2
  • x - intercept: 6

y = 12 - 6x:

  • y - intercept: 12
  • x - intercept: 2

y = 3x - 7:

  • y - intercept: -7
  • x - intercept: 7/3

Step-by-step explanation:

Hello!

Slope Intercept Form

The slope-intercept form of a line is [tex]y = mx + b[/tex]

  • y = output, ordinate
  • m = slope
  • x = input, abscissa
  • b = y-intercept

y = 1/3x - 2

The y-intercept is the "b" value of the line, given as -2.

To find the x-intercept, we simply replace the y-value with 0:

  • 0 = 1/3x - 2
  • 2 = 1/3x
  • 6 = x

y - intercept: - 2

x - intercept: 6

____________________________________________________

y = 12 - 6x

You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.

Solving for the x-intercept (remember, replace y with 0):

  • 0 = -6x + 12
  • -12 = -6x
  • 2 = x

y - intercept: 12

x - intercept: 2

____________________________________________________

y = 3x - 7

Simply take the "b" value, -7, to find the y-intercept of -7.

Solve for the x-intercept:

  • 0 = 3x - 7
  • 7 = 3x
  • x = 7/3

y - intercept: -7

x - intercept: 7/3

Additional Note:

You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.

The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.

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