Question

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)

Answer 1

Answer: last option.

Explanation:

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

`y=mx+b`

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:

`m=(-1-3)/(3-0)=-(4)/(3)`

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

`m=-(4)/(3)`

Substitute the slope and the point (-3, 2) into
`y=mx+b` and solve for "b":

`2=-(4)/(3)(-3)+b\\\\2-4=b\\\\b=-2`

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

`y=-(4)/(3)x-2`

Rewriting it in Standard form, you get:

`y+2=-(4)/(3)x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6`

Answer 2

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:

`m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}`

Then, the requested line will be of the form:

`y = - \frac {4} {3} x + b`

To find "b" we substitute the given point:

`2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2`

Finally, the line is:

`y = - \frac {4} {3} x-2`

By manipulating algebraically we have:

`y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6`

Answer:

Option D