Question

The given line passes through the points (0, ) and (2, 3).

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


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

Answer 1

D

Explanation:

Just took test and got it right :)

Answer 2

D

Explanation:

We are given a line that passes through the points (0, -3) and (2, 3).

And we want to find the equation of the line that is parallel to the given line which also passes through the point (-1, -1).

Find the slope of the given line. Recall the slope formula:

`\displaystyle m = (\Delta y)/(\Delta x)`

Hence, the slope of the line between (0, -3) and (2, 3) is:

`\displaystyle m = ((3)-(-3))/((2)-(0)) = (6)/(3) = 3`

The slope of the given line from the graph is 3.

Recall that the slopes of parallel lines are equivalent.

Hence, since the slope of the given line is 3, the slope of the parallel line must also be 3.

We are given that it passes through the point (-1, -1). Since we know the slope and a point, we can consider using point-slope form:

`\displaystyle y - y_1 = m(x - x_1)`

Where m is the slope and (x₁, y₁) is a point.

Substitute:

`\displaystyle y - (-1) = (3) (x - (-1))`

And simplify:

`\displaystyle y + 1 = 3 ( x + 1)`

In conclusion, our answer is D.