what is the x, y intecept and slope?

Question

1. 4x-12y=0
2. y=6
3. 16y-4x=-8

Answer 1

Intercepts

To find an intercept, you set the other variable equal to zero.

To find the x-int, set y = 0.
To find the y-int, set x = 0.

Slope

Easily seen when an equation is written in slope-intercept form.
y = mx + b: m is the slope and b is the y-intercept

1. 4x + 12y = 0
x-int, let y = 0

4x + 12(0) = 0
4x + 0 = 0
4x = 0

divide both sides by 4
x = 0


y-int, set x = 0
4(0) + 12y = 0
0 + 12y = 0
12y = 0

divide both sides by 12
(zero divided by anything except zero is 0. Ex. 0/1 = 0, 0/4 = 0, 5/0 = 0, 0/0 is undefined - can not do in algebra - calculus later!)

y = 0

To find the slope, rewrite #1 & #3 in slope-intercept form.
To do this solve for y ( y= mx + b)

#1.

4x + 12y = 0
4x - 4x + 12 y = -4x +0 (Subtract 4x from both sides)
12y = -4x
divide both sides by 12
y = -4/12 x
y = -1/3 x

Lets look at y = -1/3 x in comparison to y = mx + b.

y = mx + b
y = -1/3 x

m = -1/3 Since m represents slope, the slope = -1/3
There is no b, so b = 0 (which is what we found earlier by letting x = 0)

#2

y = 6 is already solved for y. Let's compare to y = mx + b

y = mx + b
y = 6

the slope = 0 (since you cannot see m in the equation, you know it is zero. Why can't we see m or x? Because zero times x equals zero)

b = 6, b represents y-intercept so the y-intercept = 6
(How do we find intercepts, setting the other variable to zero!)

#3

16y - 4x = -8

Let's get this in slope-intercept form (solve for y)
To get y by itself, we must get rid of -4x and 16
Always start farthest away, since -4x is farthest away from y

16y-4x = -8
16y-4x + 4x = 4x -8 (Add 4x to both sides)
16y = 4x - 8

divide both sides by 16

y = 4/16 x - 8/16

y = 1/4 x - 1/2 (same problem in slope-intercept form)

Compare to y = mx + b

y = mx + b
y = 1/4 x - 1/2

m = 1/4, m represents slope, so slope = 1/4
b = -1/2, b represents y-intercept, so y-intercept = -1/2

Answer 2

The equation of a staight line: y = mx + b
where m is the slope and b the y intercept
the x-intercept is given by solving for x: mx = y-b and x =(y-b)/m when y = 0, x-inter = -b/m
So
1.12y = 4x + 0
y = (1/3)x + 0
m = 1/3, y-inter = 0, x-inter = -0 = 0

2. y = 6: m = 0, y-inter = 6, x-inter = does not exist

3. 16y = 4x - 8
y = (1/4)x - 1/2
m = 1/4, y-inter = -1/2, x-inter = -(-1/2)/(1/4) = 2

Answer 3

To find the slope, change into the form y = mx + b, m is the slope and b is the y intercept. For the x intercept, let y = 0 and solve for x. It pays to graph them so you can see what's going on. That really does help your understanding.

Answer 4

1) Slope= 4/1, y-intercept is +12, x intercept is -3

2) y intercept 6, no x intercept, slope is equal to zero.

3) Slope 1/4, y intercept is -5, x intercept is 20.

lol I hope thats right I did it in my head.