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Zorluk: KolayLinear Equations and Graphing

In the standard (x,y)(x,y) coordinate plane, a line is defined by the equation 3x−2y=123x - 2y = 12. What is the sum of the xx-intercept and the yy-intercept of this line?

  1. -2Cevap
  2. B
    10
  3. C
    2
  4. D
    16
  5. E
    1

Cevap

The sum of the xx-intercept and the yy-intercept of the line is −2-2.
To find the xx-intercept, set y=0y = 0 in the equation 3x−2y=123x - 2y = 12, which gives 3x=123x = 12, so x=4x = 4. To find the yy-intercept, set x=0x = 0, which gives −2y=12-2y = 12, so y=−6y = -6. Adding these two values together gives 4+(−6)=−24 + (-6) = -2.

Adım Adım Çözüm

1
Find the xx-intercept by setting y=0y = 0 in the equation.
Substitute y=0y = 0 into 3x−2y=123x - 2y = 12 to get 3x−2(0)=123x - 2(0) = 12, which simplifies to 3x=123x = 12, yielding x=4x = 4.
The xx-intercept of a line is the point where the line crosses the xx-axis, which occurs when the yy-coordinate is 00.
2
Find the yy-intercept by setting x=0x = 0 in the equation.
Substitute x=0x = 0 into 3x−2y=123x - 2y = 12 to get 3(0)−2y=123(0) - 2y = 12, which simplifies to −2y=12-2y = 12, yielding y=−6y = -6.
The yy-intercept of a line is the point where the line crosses the yy-axis, which occurs when the xx-coordinate is 00.
3
Add the xx-intercept and yy-intercept together.
Calculate 4+(−6)=−24 + (-6) = -2.
The question asks for the sum of the xx-intercept and the yy-intercept.

Anahtar Kavram

Finding the xx- and yy-intercepts of a linear equation in standard form.
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Konular

Linear Equations and Graphing

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