MATHEMATICS: Writing the Equation of a Line?

Question

Write an equation for the line described below.


a) a horizontal line 7 units above the origin
b) a line through the origin with a slope of 5
c) a vertical line 7 units to the right of the origin
d)a line with the slope of -1 and a y-intercept of 5
e) a vertical line 4 units to the left of the origin




Kindly show all necessary and important solutions. Really need it badly Thanks.

Answer 1

a)
horizontal lines are in the form y = #.
So, since the line is "7 units above the origin"
the equation is
y = 7

b)
You have a point and slope. Use point-slope form.
Point (a, b), slope m
y - b = m(x - a)

The origin is point (0, 0).

y - 0 = 5(x - 0)
y = 5x

c)
a vertical line is in the form x = #.
so...
x = 7

d)
use slope-intercept form.
y = mx + b
(m = slope, b = y-intercept).

y = (-1)x + 5
y = -x + 5

e)
Again, vertical lines are in the form x = #.
4 units to the LEFT of the origin means (-4)
so...
x = -4

Answer 2

a. y=7
b. y=5x
c. x=7
d. y= -x + 5
e. x= -4

There's no work involved really, you just think about the line and where it is. Remember that the equation for a line generally comes in the form y=mx + b, where m=slope and b= y intercept. Also recall that a line with slope of 1 that passes through the origin has the equation y=x, and that vertical and horizontal lines are constants, ergo they don't have slopes. Good luck.

Answer 3

a) y=7
b) y=5*X
c) x=7
d) if y- intercept is in positive y-direction(means above the origin) then equation is y= -x+5 otherwise y= -x-5

e) x=-4

Answer 4

x/r + y/p =1

Answer 5

a.) y=mx+b
y=x+7
b.) y=5x+y
c.) y=7x+y
d.) y=-x+5
e.) y=4x+y

hope this is correct..I am sure at letter E!

Answer 6

a)y=7
b)x=5
c)x=7
e)x=-4

Answer 7

a)---y = 7
b)---y = 5x
c)---x = 7
d)---y = - x + 5
e)--x = - 4