Question

Find the equation of the line which passes through (-2,-2) and (2,-4).​

Answer 1

Equation of a line is given by

m (x - x¹) = (y - y¹)

• where m is the gradient
• 
  `m \: = ( {y}^(2) - {y}^(1) ) \: / ({x}^(2) - {x}^(1) )`

where (x¹ , y¹ ) and (x² , y²)

(-2,-2 ) and (2 , -4)

• m = ( -4 - (-1) ) ÷ ( 2 - (-2) )

• m = ( -4 + 1 ) ÷ ( 2 + 2 )

• m = ( -3 ) ÷ ( 4 )
• 
  `m \: = - (3)/(4)`

but equation of a line is given by

m (x - x¹) = ( y - y¹)

• 
  `- (3)/(4) (x - ( - 2)) \: = \: (y \: - ( - 2))`
• 
  `- (3)/(4) (x + 2) \: = \: (y \: + \: 2)`
• expanding the bracket

• 
  `- (3)/(4) x \: - \: (3)/(2) \: = y \: + \: 2`
• 
  `y \: = \: - (3)/(4) x \: - \: (3)/(2) \: - \: 2 \\ \\ y \: = - (3)/(4) x \: - \: (7)/(2) \\ \\ {y} \: = ( - 3x \: - \: 14)/(4)`
• 
  `multiply \: by \: 4`
• 
  `4 \: * \: y \: = 4 \: * \: ( - 3x \: - 14)/(4)`
• 
  `4y \: = \: - 3x \: - \: 14`
• Equation of the line is

• 4y = -3x - 14

Answer 2

See photo hope it helps