math- slope plz help?

Question

1. find the slope (if existing) of each of the following lines
a) 2x-2y=-3
b)y=2/3
c)x=-1
Also how do i draw y=-1/3x slope on a graph?

2. Given the line 2y=3x-6
a)find the y intercept
b)find the x intercept

Answer 1

a) -2y = -3 -2x = y =1 1/2 + x slope = 1 1/2
b) y = 2/3 slope 0
c ) x = -1 slope undefined rise/run run = 0 division by 0 undefined

y = -1/3 x try (3, -1) and (0, 0) for starts

2. 2y = 3x - 6 y = 1 1/2 x - 3

(2,0) (0, -6) x intercept = (0, -6) y intercept (2,0)


think of this a driveway is 25 feet long and it is 1 foot higher on the top than the bottom the rise is 1 foot divided by the rum 25 feet

Answer 2

Part 1(a) The slope is found by putting the equation in the
slope-intercept form, where you find y in terms of x and the
coefficients of x and y and the term on the right, -3. If we
subtract 2x from both sides, it gives -2y = -2x - 3. Now let's
divide both sides by -2 and we get: y = x + 1½
The coefficient of x here is 1, so the slope of the line is 1.
(b) The slope is the ratio of dy to dx, where dy is the change
in the value of y and dx is the change in the value of x. For a
constant y, in this case y = 2/3, dy is zero since the value of
y never changes, thus the slope is zero.
(c) By the same token, the slope of x = -1 is undefined, since
the value of x never changes, meaning dx = 0 and we cannot
divide by zero. The graph of x = -1 is a vertical line parallel
to the y-axis and intercepting the x-axis at -1.
To draw the graph of y = -1/3x, it is given in slope-intercept
form; that is, its slope is negative 1/3. When x = zero,
y equals zero, so the line passes through the origin and
goes up one unit in the same distance it goes left three units.
For question 2, again put the equation in slope-intercept
form by dividing both sides by 2. You get: y = 3/2 x - 3.
The y-intercept is -3. To get the x-intercept, let y = 0
since y is zero everywhere on the x-axis.
If 0 = 3/2 x - 3, then 3/2 x = 3, and x = 2.
The x-intercept is 2.

Answer 3

1. Convert it to the y=mx+b which is the slope intercept form.
The "m" is your slope and "b" is your y intercept.
a. 2x-2y= - 3
1. Move 2x to the other side then it becomes -2y=-2x - 3
2. Now divide both sides by -2 so it becomes y= 1x + 3/2
3. Look at the form, you will see that your slope is 1.

b. y= 2/3
this graph is a horizontal line. Horizontal lines have a slope of 0.

c. x= - 1
this graph is a vertical line. vertical lines have no slope.

2. The y intercept is the point at which the line crosses the y axis and x intercept is the point at which the line crosses the x axis. To find the y intercept, you plug in 0 for x and solve for y.
To find the x intercept, you plug in 0 for y and solve for x.

2(0)=3x-6 ---> 0=3x - 6 ---> 6=3x --->x=2 is your x intercept.
2y=3(0)-6 ---> 2y= -6 ----> y= -3 is your y intercept

Answer 4

1
a) you want to put this in y=mx + b form(m is the slope).
-2y = -2x - 3
y = (1)x + 2/3
The slope is 1.
b) y = 2/3: this is a horizontal (flat)line so the slope is 0.
c) x = -1: This is a straight up and down line(undefined) so it does not exist.

2. put in y=mx+b (m=slope, b=y-intercept)
y = (3/2)x - 3
a) -3
b) the x intercept is when y=0 so substitue 0 for y and solve:
2(0) = 3x - 6
0 = 3x - 6
6 = 3x
x = 2 is where the line intercepts x.

Answer 5

(1):

2x-2y=-3
-2y=-2x-3
y=x+1.5
slope = 1

y=2/3
slope = 0

x=-1
slope does not exist



(2)

set x = to 0:
2y=3x-6
y=1.5x-3
y-intercept = -3

set y = to 0:
(0)=1.5x-3
3=1.5x
x-intercept = 2

Answer 6

a) 2x = 2y-3 gradient of 1
b) infinity, a straight horizontal line
c) undefined, it's a straight line
intersecting (0,0), and use the point, (1,-3)

2a) x=0
2y = -6
y = -3
b) y=0
3x = 6
x=2

Answer 7

Here's answer for question no. 2:

2y=3x-6
y=3x-6/2
y=3x-3

and

2y=3x-6
2y+6=3x
(2y+6)/3=x
2y+2=x
therefore, x=2y+2