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).