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Use the information given to answer the question.

Consider the equation of a line.
-3x + y = -10
What is the y-intercept of the line that is parallel to -3x + y = -10 and passes through the point (-2,-4)?
O (0,-4)
O (0,-2)
O (0,2)
O(0,4)

User GolfARama
by
8.4k points

1 Answer

6 votes

Answer: (0, 2)

Explanation:

To find the y-intercept of a line parallel to -3x + y = -10, we need to determine the equation of the parallel line using the given information.

The given line, -3x + y = -10, is in the standard form of a linear equation, which is Ax + By = C, where A, B, and C are constants.

First, we need to rearrange the given equation to isolate y:

-3x + y = -10

y = 3x - 10

The slope of the given line is 3. Since the line we are looking for is parallel, it will have the same slope.

Using the point-slope form of a linear equation, we can write the equation of the parallel line:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point (-2, -4), and m is the slope.

Plugging in the values, we get:

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

y + 4 = 3(x + 2)

Expanding and simplifying, we get:

y + 4 = 3x + 6

To find the y-intercept, we set x = 0 and solve for y:

y + 4 = 3(0) + 6

y + 4 = 6

y = 6 - 4

y = 2

Therefore, the y-intercept of the line parallel to -3x + y = -10 and passes through the point (-2, -4) is (0, 2).

User Namoscato
by
9.0k points

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