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:

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.