Question

On a coordinate plane, a line goes through (0, 3) and (3, negative 1). A point is at (negative 3, 2). 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

Answer 1

Step-by-step explanation:

equatiin of line L1;y-y1=m(x-x1)

m=y2-y1/x2-x1=-1-3/3-0=-4/3

the two lines are parallel

m1=m2

L2;y-y1=m(x-x1)

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

3y-6=-4x-12

3y+4x=-6 is equation of parrallel lines.

Answer 2

The equation of the line with the given conditions is:

$4x + 3y = -6$

The equation of a line is given by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change.
• b is the y-intercept, which is the value of x when y = 0.

If two lines are parallel, they have the same slope.

The slope is the change in y divided by the change in x. Parallel to a line with points (0,3) and (3,-1), thus:

$m = \frac{-1 - 3}{3 - 0} = -\frac{4}{3}$

Thus:

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

Passes through point (-3,2), which means that when $x = -3, y = 2$, and this is used to find b.

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

$4 + b = 2$

$b = -2$

Then

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

Placing it into standard form:

$3y = -4x - 6$

$4x + 3y = -6$

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