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Zorluk: OrtaLinear Equations in Two Variables

In the xyxy-plane, the graph of the linear equation y−4=m(x+2)y - 4 = m(x + 2) contains the point (6,8)(6, 8), where mm is a constant. What is the value of the xx-intercept of the line?

  1. -10Cevap
  2. B
    -6
  3. C
    -4
  4. D
    5

Cevap

-10
The correct answer is −10-10. By substituting the point (6,8)(6, 8) into the equation y−4=m(x+2)y - 4 = m(x + 2), we obtain 8−4=m(6+2)8 - 4 = m(6 + 2), which simplifies to 4=8m4 = 8m, giving m=0.5m = 0.5. Using this value of mm, the equation of the line is y−4=0.5(x+2)y - 4 = 0.5(x + 2). The xx-intercept is the value of xx when y=0y = 0. Substituting 00 for yy gives −4=0.5(x+2)-4 = 0.5(x + 2), which simplifies to −8=x+2-8 = x + 2. Solving for xx gives x=−10x = -10.

Adım Adım Çözüm

1
Substitute the given point (6,8)(6, 8) into the equation to find the value of the constant mm.
8−4=m(6+2)⇒4=8m⇒m=0.58 - 4 = m(6 + 2) \Rightarrow 4 = 8m \Rightarrow m = 0.5
Since the line passes through the point (6,8)(6, 8), these coordinates must satisfy the equation.
2
Write the completed equation of the line using the value of mm.
y−4=0.5(x+2)y - 4 = 0.5(x + 2)
Substituting m=0.5m = 0.5 back into the original point-slope equation gives the specific line.
3
Find the xx-intercept by setting y=0y = 0 and solving for xx.
0−4=0.5(x+2)⇒−4=0.5x+1⇒−5=0.5x⇒x=−100 - 4 = 0.5(x + 2) \Rightarrow -4 = 0.5x + 1 \Rightarrow -5 = 0.5x \Rightarrow x = -10
The xx-intercept of a graph is the point where the graph crosses the xx-axis, which occurs where y=0y = 0.

Anahtar Kavram

Finding the intercepts and slope of a linear equation in two variables
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Konular

Linear Equations in Two Variables

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