Find the equation of the line parallel to the line 3x + y = 5 and containing the point (4, – 2).
I would choose B. Am I correct?
All lines parallel to
3x+y=5
can be written as
3x+y=k
where k is a value to be found.
Since it passes through (4,-2), we only have to substitute x=4, and y=-2 into the general equation:
3(4)+ (-2) =k
from which we obtain k=12-2=10
Thus the required line is
3x+y = 10
If you have a list of choices:
A. y = -3x - 2
B. y=-3x+10
C. y=1/3x-10/3
D. y=3x-14
which one would you choose?
Correct!
Thank you!
To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to find the equation of the parallel line.
Step 1: Find the slope of the given line.
The given line is in the standard form Ax + By = C. To find the slope, we need to rearrange the equation into slope-intercept form y = mx + b, where m is the slope.
Rearranging 3x + y = 5, we get y = -3x + 5.
Comparing this equation with the slope-intercept form, we see that the slope of the given line is -3.
Step 2: Use the slope to find the equation of the parallel line.
The slope of a parallel line is the same as the slope of the given line, which in this case is -3. We also have a point (4, -2), which the parallel line must contain.
We can use the point-slope form of a line to find the equation of the parallel line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting the given values into the point-slope form, we have:
y - (-2) = -3(x - 4)
y + 2 = -3(x - 4)
y + 2 = -3x + 12
y = -3x + 10
Therefore, the equation of the line parallel to 3x + y = 5 and containing the point (4, -2) is y = -3x + 10.