Answer:
C. y = 2x - 3 and 3x + 6y = 12
Step-by-step explanation:
The line with a positive gradient passes through (0, -3) and (2, 1)
The gradient of this line = Change in y ÷ change in x
= (1 - - 3) ÷ (2 - 0) = 4/2 = 2
The equation of this line is;
[tex]\frac{y + 3}{x - 0}[/tex] = 2
y = 2x - 3
The line with a negative gradient passes through (0, 2) and (2, 1)
The gradient of this line = Change in y ÷ change in x
= [tex]\frac{1 - 2}{2 - 0} = -\frac{1}{2}[/tex]
The equation of this line is;
[tex]\frac{y - 2}{x - 0} =- \frac{1}{2}[/tex]
y = [tex]-\frac{1}{2}[/tex]x + 2
y + [tex]\frac{1}{2} x[/tex] = 2
Multiplying by 6 throughout gives;
3x + 6y = 12
