Question

which equation of the line through (-1, -4) and the parallel to the line 3x + y = 5?

a. y = 3x + 1
b. y = -3x - 7
c. y = 3x - 1
d. y = -3x + 7

Answer 1

To find the equation of the line that goes through the point (-1, -4) and is parallel to the line given by the equation \(3x + y = 5\), we first need to determine the slope of the given line.

1. Rearranging the given line equation \(3x + y = 5\) into slope-intercept form (y = mx + b):
\[
y = -3x + 5
\]
The slope (m) of this line is \(-3\).

2. Since we want a line that is parallel, it will have the same slope. Therefore, our new line will also have a slope of \(-3\).

3. Now we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point (-1, -4) and \(m = -3\).

4. Plugging in the values:
\[
y - (-4) = -3(x - (-1))
\]
Simplifying:
\[
y + 4 = -3(x + 1)
\]
\[
y + 4 = -3x - 3
\]
\[
y = -3x - 3 - 4
\]
\[
y = -3x - 7
\]

The equation of the line through (-1, -4) and parallel to the line \(3x + y = 5\) is \(y = -3x - 7\).

Therefore, the correct answer is:
**b. \(y = -3x - 7\)**.