algebra 1 , functions
algebra 1 , functions
What we know about parallel lines is that they have the same slope, but not the same y-intercept. What the problem wants you to do is find your y-intercept.
The equation given is: 4x+y-1=0
A lot of people like to see equations like this: y=mx+b
So lets put it that way!
4x+y-1=0 is the same as y= -4x+1
For this particular equation, b=1, but for a line with slope -4 that goes through the point (1,2), the y-intercept changes.
Now we have: y= -4x+b
Plug'n'chug the point into the equation above to get: 2=-4(1)+b
Now solve for b to get b=6.
Your equation is now: y= -4x+6 or 4x+y-6=0.
If you don't agree or understand your answer, it is always a good idea to check your answer by plugging your point back in and see if it makes sense.
4(1)+2-6 = 4+2-6 = 6-6 = 0
A quick way:
4x + y = 4*1+2 = 6
Ideas: If a line passes the point (x_{o}, y_{o}) and parallel to the second line Ax+By = C, then the equation of the first line is Ax+By = Ax_{o}+By_{o}.
First, solve the equation for y to put it in slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept, the point where it crosses the y-axis.
4x + y - 1 = 0
y = -4x + 1
The slope m is -4. Parallel lines have the same slope!
Then you can use the point-slope form of the equation for a line to find the answer:
y - y_{1} = m(x - x_{1})
where (x_{1}, y_{1}) is the known point.
The known point is (1, 2), so...
y - 2 = -4(x - 1)
y = 2 - 4x + 4
y = -4x + 6
Check your work:
The slope is the same as the original line, so the lines are parallel.
Plug in the known value for x and verify that y is correct:
2 =? (-4)(1) + 6
2 =? - 4 + 6
2 = 2
Note: You don't have to memorize the point-slope form for a line if you remember that the definition of slope is the change in y divided by the change in x between two points on the line:
(y-y_{1}) / (x-x_{1}) = m
(y-y_{1}) = m(x-x_{1})
where (x_{1}, y_{1}) is a starting point and (x, y) is some second point.
Step 1 We arrange the equation 4x+y-1=0 to make y=mx+b to find the slope and we do this by soliving for y.
4x+y-1=0 we subtract 4x for both sides
-4x =-4x and should give us
y-1= -4x now we add one to both side of the equations
+1 = +1 this should give us
y= -4x+1
by solving for y we discovered that our slope m is equal to -4
now we are ready for step 2 to find the equation of the line that is parallel we keep the same slope and we use (1,2) to solve our problem and use the equation mention above
we said that x = 1
y = 2
we rewrite our equation in the following form
y=-4x+b and substitute for our values
2=-4(1)+b
2=-4+b add 4 in both side
+4 = +4 and shall give us
6= b
Our parallel equation shall be
y = -4x + 6
Next we check for our answer
we use our values
2= -4(1)+6
2=-4+6
2=2
I hope my answer would be useful for you
y = -4x + 1
Slope = m = -4
x = 1, y = 2
y = -4x + b
b = y + 4x = 2 + 4(1)