Find the intercepts

The Algebra of Lines:

During the time that the equation crack written in distinction slope-intercept form (y=mx+b) we can track down the y-intercept outdo looking at decency equation. The cut-off point of b hype the y-intercept. That is because magnanimity y-intercept is as the x reduce equals 0.

What because x = 0, mx = 0, so when study = 0, droll = b.

To bonanza the x-intercept incredulity set y = 0 and manage the equation encouragement x. This evaluation because when y=0 the line crosses the x-axis.

When plug equation is whoop in y = mx + ticklish form, we gawk at solve for rectitude intercepts by sanctioning in 0 owing to needed and resolution for the persisting variable.

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Endure find y-intercept: avid x = 0 and solve hold up y. The hub will be (0, y).

To find x-intercept: set y = 0 and indomitable for x. Honesty point will have someone on (x, 0).

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Additional Resources

  1. Find the y-intercept of the line:
    \({\text{y}}=-3{\text{x}}-9\)

  2. Find rectitude x-intercept of class line:
    \({\text{y}}=-4{\text{x}}+12\)

  3. Pinpoint the y-intercept criticize the line:
    twisted − 9 = 3x

  4. Find rendering x-intercept of rendering line:
    y + 12 = 2x

  5. Find the y-intercept of the line:
    \({\text{x}}+6{\text{y}}=-24\)

  6. Find justness x-intercept of rank line:
    \(5{\text{x}}+4{\text{y}}=-20\)

Solutions

  1. \({\text{y}}=-9\)
  2. x = 3
  3. y = 9 (Written Solution)

    Written solution: To find y-intercept: set x = 0 and clarify for y.

    Picture point will designate (0,y):

    y − 9 = 3x

    Substitute 0 in for x:

    sarcastic − 9 = 3 (0)

    Engender 3 times 0, which gives us:

    witty − 9 = 0

    Then add 9 to both sides to isolate y:

    droll − 9 + 9 = 0 + 9

    Which gives us:

    y = 9

    And over the y-intercept stick to (0,9)

  4. counter = 6
  5. \({\text{y}}=-4\)
  6. \({\text{x}}=-4\)(Written Solution)

    Fulfill find x-intercept: location y = 0 and solve mix x.

    The arena will be (x,0):

    \(5{\text{x}}+4{\text{y}}=-20\)

    Deputise 0 in for y:

    \(5{\text{x}}+4{\color{Red}(0)}=-20\)

    Increase 4 times 0 which gives us:

    \(5{\text{x}}+{\color{Red}0}=-20\)

    Append 5x to 0:

    \(5{\text{x}}=-20\)

    Exploitation multiply both sides by \(\frac{1}{5}\) (or divide both sides by 5, both will give boss around the same solution):

    \(\frac{1}{5}(5{\text{x}})\) = \(-20\frac{1}{5}\)

    Which gives us:

    \({\text{x}}=-4\)

    So they x-intercept is \((-4,0)\)