Write the standard form of the equation of the line parallel to the graph of 9x + 3y = 6 that passes through (0,3). SHOW YOUR WORK

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

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