what is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
visible line: (0,3)(3,-1)

For this case we have that by definition, if two lines are parallel their slopes are equal.

The line given for the following points:

(0,3) and (3, -1). Then the slope is:

Then, the requested line will be of the form:

To find "b" we substitute the given point:

Finally, the line is:

By manipulating algebraically we have:

Option D

last option.

Step-by-step explanation:

 The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:

Since the other line is parallel to this line, its slope must  be equal:

Substitute the slope and the point (-3, 2) into and solve for "b":

Then, the equation of the other line in Slope-Intercept form is:

Rewriting it in Standard form, you get:

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