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Which equation represents a line that passes through (–9, –3) and has a slope of –6? a y – 9 = –6(x – 3) b y + 9 = –6(x + 3) c y – 3 = –6(x – 9) d y + 3 = –6(x + 9)

Answer :

ThinkingOutLoudgo

Slope intercept form of line -

[tex]y - y_1 = m(x - x_1)[/tex]

y1 = y - coordinate of point

x1 = x - coordinate of point

m = slope of line

  • [tex]y -(- 3) = - 6(x - (- 9))[/tex]
  • [tex]y + 3 = - 6(x + 9)[/tex]
  • [tex]y + 3 = - 6x - 54[/tex]
  • [tex]y + 6x = - 54 - 3[/tex]
  • [tex]y + 6x = - 57[/tex]
  • [tex]6x + y + 57 = 0[/tex]

Correct option is : -

D. y + 3 = -6(x + 9)

Semsee45go

Answer:

[tex]\textsf{d)} \quad y+3=-6(x+9)[/tex]

Step-by-step explanation:

Point-slope form of a linear equation:

[tex]\boxed{y-y_1=m(x-x_1)}[/tex]

Where:

  • m is the slope.
  • (x₁, y₁) is a point on the line.

Given information:

  • Slope = -6
  • Point = (-9, -3)

Substitute the given values into the formula:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\implies y-(-3) & =-6(x-(-9))\\y+3 & =-6(x+9)\end{aligned}[/tex]

Therefore, the equation that represents a line that passes through (-9, -3) and has a slope of -6 is:

[tex]\boxed{y+3=-6(x+9)}[/tex]

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