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
• $m \: = ( {y}^{2} - {y}^{1} ) \: \div ({x}^{2} - {x}^{1} )$

where (x¹ , y¹ ) and (x² , y²)

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

• m = ( -4 - (-1) ) ÷ ( 2 - (-2) )

• m = ( -4 + 1 ) ÷ ( 2 + 2 )

• m = ( -3 ) ÷ ( 4 )
• $m \: = - \frac{3}{4}$

but equation of a line is given by

m (x - x¹) = ( y - y¹)

• $- \frac{3}{4} (x - ( - 2)) \: = \: (y \: - ( - 2))$
• $- \frac{3}{4} (x + 2) \: = \: (y \: + \: 2)$
• expanding the bracket

• $- \frac{3}{4} x \: - \: \frac{3}{2} \: = y \: + \: 2$
• $y \: = \: - \frac{3}{4} x \: - \: \frac{3}{2} \: - \: 2 \\ \\ y \: = - \frac{3}{4} x \: - \: \frac{7}{2} \\ \\ {y} \: = \frac{ - 3x \: - \: 14}{4}$
• $multiply \: by \: 4$
• $4 \: \times \: y \: = 4 \: \times \: \frac{ - 3x \: - 14}{4}$
• $4y \: = \: - 3x \: - \: 14$
• Equation of the line is

• 4y = -3x - 14

Answer 2

See photo hope it helps