Find the equation of the line parallel to the line 3x + y = 5 and containing the point (4, – 2).
This is what I got. Is this correct?
y = –3x + 10
Yes!
Is my evvaluation correct?
y=mx+b
3x + y = 5
y = -3x+5
y = -2
m = -3
x = 4
b = unknown
Solve For b:
y = -3x + b
-2 = -3(4) + b
-2 = -12 + b
-12 + 10 = -2
10=b
To Check:
y = -3x + b
-2 = -3(4) + b
-2 = -12 + b
-12+10 = b
10 = b
-2 = -3(4) + b
-2 = -12 + 10
-12+10 = -2
b = 10
A real easy way to do this question is to realize that since they have the same slope, the equations must differ only in the constant.
So let the new equation be
3x + y = c
plug in the point (4,-2)
12 - 2 = c = 10
so your equation is 3x + y = 10
[ BTW, had it asked for a perpendicular line then my opening new equation would have been
x + 3y = c
(notice the slopes would be opposite reciprocals) ]
So my work is correct? Thanks for the help!
To find the equation of a line parallel to another line, you need to know that parallel lines have the same slope.
The given line equation is 3x + y = 5. To use this equation, you want to rewrite it in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.
Let's start by rearranging the equation to isolate y:
y = -3x + 5
From this equation, we see that the slope (m) of the given line is -3.
Since the line parallel to this line has the same slope, our new line will have a slope of -3 as well.
Now we can proceed to find the equation of the line passing through the point (4, -2) with a slope of -3.
Using the point-slope form, the equation is:
y - y1 = m(x - x1)
Plugging in the values, we have:
y - (-2) = -3(x - 4)
Simplifying further:
y + 2 = -3x + 12
Finally, rearranging this equation to slope-intercept form to get the equation of the line:
y = -3x + 10
Therefore, the equation of the line parallel to 3x + y = 5, and passing through the point (4, -2), is y = -3x + 10.
So, your answer is correct!