Answer:
y + 3x = 3
Step-by-step explanation:
Standard Form of the Equation of a Line
The equation of a line in standard form is:
Ax + By = C
Where A, B, and C are constants.
The equation of a line can also be expressed in slope-intercept form, where m is the slope, and b the y-intercept:
y = mx + b
Two lines are parallel if they have the same slope, that is if m1 is the slope of a given line, and m2 is the slope of a parallel line, then m2=m1.
We are given the line:
9x + 3y = 6
Dividing by 3:
3x + y = 2
Solving for y:
y = -3x + 2
The slope of this line is m1=-3, thus the slope of the required line is also m2=-3.
The equation of that required line is:
y = -3x + b
We still don't have the value of b. To find it, we substitute the coordinates of the given point (0,3):
3 = -3(0) + b
Thus, b = 3.
The required equation of the line is:
y = -3x + 3
To write it in standard form, we add 3x:
y + 3x = 3
