Find the equation of a line?

ok if it is parallel, then it has the same slope, so we know that the line you are looking for has

slope: 3/4
and a point at (1,7)

then plug these values into the basic line form:

y=mx+b
7=3/4(1) + b
7= 3/4 + b
7-3/4 = b
28/4 - 3/4= b
25/4 = b

then put that and the slope back into the line form, so your answer is:

y=3/4x+ 25/4 or,
y=3/4x + 6 1/4

You have all you need. Since the lines are parallel they will have the same slope. This is because slope is rise over run. Next the problem tells you the 2nd line goes though (1, 7) Next solve for the y intercept or b. If you insert the point into the equation y=3/4x+b, you get 7=3/4*1+b, now solve for b. b= 6.25. Your equation should be y=3/4x+6.25.

if it is parallel to y=3/4x+5 then the gradients are the same

therefor
m=3/4 and goes through point (1,7)

y=mx+c
7=(3/4)(1)+c
7=(3/4)+c
c=6 1/4

therefor as m=3/4 and c=6 1/4 or 25/4

equation is

y=3/4x+25/4

Find the slope of the given line y = 3/4x + 5 first.
by using slope-intercept form y = mx + b
the slope of the given line is 3/4

parallel mean equal slope

then we can use slope-point form to find the new equation.

point is (1,7) which is given. Slope is 3/4 that we found above

y - y1 = m ( x - x1 ) ( x1,y1) is the given point
y - 7 = 3/4 * ( x- 1 ) ( distribute it )
y - 7 = 3/4 x - 3/4 ( add the 7 to the right side )

y = 3/4x -3/4 + 7 ( combine the -3/4 and 7)

y = 3/4x + 6 1/4 ( mixed fraction )

Two non vertical lines are parallel if and only if their slopes are equal.
Y=3/4x +5
Y=mx+b
where m is the slope of the line and b is the y intercept of the graph of the line.

So we know that m=3/4
We now use the point slope form to find the equation of the line with slope. An equation of a line through a point P(x1 , y1) with slope m is given by
y - y1 = m(x - x1)
y-7=3/4(x-1)
Y-7=3/4x-3/4
Y=3/4x-3/4+7
Y=3/4x+25/4

General form of an equation of a line:
y = mx + c
where m is the gradient and c is the y-intercept

When 2 lines are parallel, their gradients are equal.

The equation of the line that you are looking for is parallel to y = 3/4x + 5
y = (3/4)x + 5
gradient, m = 3/4

So the gradient of the line is also 3/4.
Now we have m = 3/4 and point (1, 7)
Substitute the point given and the gradient into the general form:
y = mx + c
7 = (3/4)(1) + c
7 = 3/4 + c
c = 7 – 3/4
c = 25/4

Therefor the equation of the line is:
y = (3/4)x + 25/4


Done

u have to consider two equations for st. line,
one equation y-y1=m(x-x1)
now u have got points x1 and y1 given to u i.e (1,7) i.e
x1=1 and y1 =7 put the value in equation
y-y1=m(x-x1)
=y-7=m(x-1)
problem is it will be solved if we have the value of m,
now compare another equation of line, i.e
y=mx+c
u r given y = 3/4x+5
if u compare both the equation u will find that m =3/4
now put the value of m in above equation.i.e

y-7=m(x-1)
=y-7=3/4(x-1)

multiply both sides by 4 i.e = 4y-28=3x-3 re arranging the terms
3x-4y+25=0

is the answer,

m = 3/4
(1,7)

y - 7 = (3/4) ( x - 1 )

y = (3/4) x - 3/4 + 7

y = (3/4) x + 25/4