math problem?

Question

find an equation for the line with the given properties. Express the answer using the general form or the slope-intercept form, whichever you prefer.

Parallel to the line y = 4x; containing the point (-1,2)

can you explain how you solve this

Answer 1

for lines to be parallel their slopes must be equal
y=4x m1=m2=4
y-y1=m2(x-x1)
y-2=4(x-(-1))
y-2=4x+4
y=4x+6

another solution
slope intercept form
since line 1 is parallel with line 2
y=4x+b is the general equation for the family of lines
with slope of 4
at P(-1,2) c is
2=4(-1)+c;c=6
therefore line 2 has an equation of
y=4x+6

Answer 2

If the line is parallel to y=4x then it has the same gradient.

So the line is of the form y=4x+c (c is a constant)

It goes through the point x=-1 and y=2 so put these in the above equation to work out c

2=4*-1 +c => 2=-4+c =>c=6

So the equation of the line is y=4x+6

Answer 3

Any line parallel to y = 4x will have equation of the form
y = 4x + k.
As the required line passes through the point ( - 1, 2),
2 = 4( -1) + k
=> k = 6
Hence the equation of the required line is
y = 4x + 6.

Answer 4

Parallel lines have equal slopes.

y = mx + c
y = 4x
m = 4

Slope of the line is 4
The line passes through (-1,2)
y = 4x + c
2 = -4 + c
c = 6

y = 4x + 6

Answer 5

theory : parallel lines has same slopes.

so, if you are going to make parallel lines for a given line, get the slope first.

then try y=mx+c //m==slope

put the given point s, and m

Answer 6

to be parallel

y = 4x + c

c = 6

y = 4x + 6