Find the equation of the line parallel to the line 3x + y = 5 and containing the point (4, – 2)
Take your original equation (3x+y=5) and put it in y=mx+b form. You should get y=-3x+5. The slope is 3.
What's the slope of a line that is parallel to y=-3x+b? Do you have a point to substitute into that equation to get a y-intercept?
Would these be the points from the original equation?(4, – 2)
I also have some possible answers
A. y = -3x - 2
B. y=-3x+10
C. y=1/3x-10/3
D. y=3x-14
I say it's B but am not sure
Yes, that would be the point to use, and yes, it's B.
y = -3x + b
(-2) = -3(4) + b
-2 = -12 + b
10 = b
C and D couldn't even be possibilities because their slopes are not -3. A doesn't work once you plug in the point.
Thanks Amy!
thanks Amy.
To find the equation of a line parallel to another line, we need to determine the slope of the given line and use it to find the equation of the parallel line. Then, we can use the given point to find the specific equation.
First, let's find the slope of the given line. The equation of the line can be rewritten in slope-intercept form (y = mx + b), where m is the slope:
3x + y = 5
y = -3x + 5
Comparing this equation to the slope-intercept form, we can see that the slope (m) is -3.
Since the parallel line will have the same slope, the equation of the parallel line will also have a slope of -3. Using the point-slope form (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point:
y - (-2) = -3(x - 4)
Simplifying the equation:
y + 2 = -3x + 12
Rearranging the equation to the standard form (Ax + By = C):
3x + y = 10
Hence, the equation of the line parallel to 3x + y = 5 and containing the point (4, -2) is 3x + y = 10.