Question

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 1

Slope intercept form of line -

`y - y_1 = m(x - x_1)`

y1 = y - coordinate of point

x1 = x - coordinate of point

m = slope of line

• 
  `y -(- 3) = - 6(x - (- 9))`
• 
  `y + 3 = - 6(x + 9)`
• 
  `y + 3 = - 6x - 54`
• 
  `y + 6x = - 54 - 3`
• 
  `y + 6x = - 57`
• 
  `6x + y + 57 = 0`

Correct option is : -

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

Answer 2

`\textsf{d)} \quad y+3=-6(x+9)`

Explanation:

Point-slope form of a linear equation:

`\boxed{y-y_1=m(x-x_1)}`

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:

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

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

`\boxed{y+3=-6(x+9)}`