Question

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)

Answer 1

Answer:

D). y – 1= Three-halves(x + 3)

Step-by-step explanation:

Took the test

Answer 2

The equation of the line is given by:

$y - 1 = \frac{3}{2}(x+3)$

Which is the fourth option.

------------

The equation of line, in point-slope form, is given by:

$y - y_0 = m(x - x_0)$

In which:

• m is the slope, that is, the rate of change.
• The point is $(x_0,y_0)$
• If two lines are parallel, they have the same slope.

------------

• The given line has two points, (-2,-4) and (2,2).
• The slope is given by the change in y divided by the change in x.
• Change in y: -2 - (-4) = 2 + 4 = 6
• Change in x: 2 - (-2) = 2 + 2 = 4
• Slope: $m = \frac{6}{4} = \frac{3}{2}$

Thus:

$y - y_0 = \frac{3}{2}(x - x_0)$

------------

• Point (-3,1) means that $x_0 = -3, y_0 = 1$, and thus:

$y - y_0 = \frac{3}{2}(x - x_0)$

$y - 1 = \frac{3}{2}(x - (-3))$

$y - 1 = \frac{3}{2}(x+3)$

Fourth option.

A similar problem is given at https://brainly.com/question/22532445