find the equation of the line passing through?

Question

(1,8) and parallel to y-2x=9 explain thoroghly please.

can some also show me

the equation of a line passing through
(1, - 6 and perpendicular to y=1/2x + 7

Answer 1

*You need to know the slope-intercept form which is,
y = mx + b

First: write the equation in slope-intercept form: add 2x to both sides in order to isolate "y" on one side...

y - 2x + 2x = 9 + 2x
y = 9 + 2x
y = 2x + 9

*The slope is a fraction/whole number beside the "x" which is, 2 in this equation. A line parallel to the given equation has the same slope: 2

Sec: place the slope & given point in the point-slope intercept form...

y - first y = m(x - first x)
y - 8 = 2(x - 1)
y - 8 = 2x - 2

Third: add 8 to both sides...

y - 8 + 8 = 2x - 2 + 8
y = 2x + 6

Answer 2

The answer is y = 2x + 6.

In the general equation for a line:
y = mx + b, m is the slope of the line and b is the y - intercept (what y equals when x = 0.)
The line must be parallel to y - 2x = 9.
Rearranging this to general form,
y = 2x + 9.
You therefore know the slope of the line is 2. For two lines to be parallel, they must have the same slope and cannot be the same line. You then know that the line you are looking for has the same slope of 2.
Going back to the general form of a line, your line will have the equation:
y = 2x + b. (replacing m with the known slope 2)
You know it passes through the point (1,8) so plug those into your general equation.
8 = 2(1) + b.
b = 6
So the equation of the line is y = 2x + 6.

Answer 3

since y=2x+9 is parallel to (1,8) they will have the same slope.
y=mx+b with m being the slope.
y=2x + b solve b using (1,8)
b=6
Equation will be y=2x+6

Answer 4

Whoops...need to be more careful...the next folks are right...I have corrected mine so do not vote for me.

First line is y=2x+9. Slope is 2.

8 = 1*2 +b

b = 6

y = 2x + 6

Answer 5

y=2x+9

parallel must have a same slope.
y=mx+b
8=2(1)+b
8=2+b
b= 6
y=2x+6