Respuesta :
Answer:
The equation of line g is y = x/3 + 5
Step-by-step explanation:
Given that the line d passes through the points (-3, 1) and (9, 5) we have the equation of line d in slope and intercept form., y = m·x + c found as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) = (-3, 1)
(x₂, y₂) = (9, 5)
[tex]Slope, \, m =\dfrac{5-1}{9-(-3)} = \dfrac{4}{12} = \dfrac{1}{3}[/tex]
The line, d, in point-slope form is y - 1 = 1/3(x - (-3))
Which gives;
y - 1 = 1/3·x + 3/3
y = 1/3·x + 1 + 1 = 1/3·x + 2
Given that line g is parallel to line d, we have;
Slope of line g = slope of line d = 1/3
Therefore, the equation of line g passing through point ^6, 7) in point-slope form is y - 7 = 1/3(x - 6) which gives;
y = x/3 - 2 + 7 = x/3 + 5
The equation of line g is y = x/3 + 5
The line f passing through point (-3, -3) is perpendicular to ling g, therefore, the slope = -1/m = -1(1/3) = -3
The point-slope form of the equation is y -(-3) = -3(x - (-3)) which gives;
y + 3 = -3·x - 9
Therefore, the equation of line f is y = -3·x - 9 - 3 = -3·x - 12
The equation of line f is y = -3·x - 12.
