confused about x and y intercepts...?

Question

I have two homework questions on the x and y intercepts in graphing but I'm extremely confused. when its all written out I somewhat understand it, however I just can't get these two questions. Could someone please help me??

Question 1) What is the x-intercept of the line 3x + 5y = 2. The choices are (2,0) or (3,2) or (2/3, 0) or (0, 2/5). I selected (3,2) however I'm not positive about that answer.

Question 2) find the x-intercept and the y-intercept of the line
3x - y = 9.
x-intercept = ?, ?
y-intercept= ?, ?
I can't seem to figure this one out AT ALL and I tried 3 diff. ways.

If someone could possibly help with this third question I would extremely appreciated as well.
Question 3)complete the table so that the coordinates of the ordered pairs in the table satisfy 3x - 2y = 24
x | y
____
0 | ?
? | 3
2 | ?
8 | ?
? | -3
I've tried this one over and over and I've gone through 2 sheets of graph paper and I can't seem to figure it out. any help is appreciated!!

Answer 1

you're looking at it the wrong way..

I think there's an intercept form for the equation of a line which states it simply:

consider a line where the x-intercept is (a,0)and the y intercept is (0,b)
then the equation of the line comes to:

(x/a)+(y/b)=1
Now reducing the euation of a straight line to this form will automatically give you the intercepts on both axes.
x-intercept is the point at which the line cuts the x-axis and so is of the form (a,0) as it is found by considering y=0.
similarly the y-intercept is found by considering x=0 in th eequation of the line and thus will always be a point of the form(0,b)

now let's answer the question:
1. reducing RHS constant to 1 we get:
3x/2+5y/2=1
or, x/(2/3)+y/(2/5)=1
thus the x-intercept is (2/3,0) andth ey-intercept is (0,2/5)

2. 3x-y=9(given)
3x/9-y/9=1 (reducing RHS-Right Hand Side to 1 by dividing both sides by 9)
x/3 + y/(-9)=1

thus th ex-intecept is (3,0) and the y-intercept is (0,-9)

3. this does not need graph paper...all you need to do is put the values for x and y and solve the equation for the value of y and x respectively...

x | y
-----------
0 | ?(-12) (putting value we get -2y=24)
?(10)| 3 (putting the value of y=3 we get: 3x-6=24 or 3x=30 or x=10)

continue similarly for the rest...
all the best...

Answer 2

Basically you have to use the equation of a line y = mx + b. Sometimes you have rearrange the equation. To find the intercept of x just set y to zero and solve. To find the y intercept set x to zero and solve.

The first solution is:
3x + 5(0) = 2
3x = 2
x = 2/3
so the intercept is (2/3,0)

The second solution is 3x - y = 9
x-intercept is
3x - 0 = 9
x = 9/3
x = 3, x intercept is (3,0)
y-intercept is
3(0) - y = 9
y = -9, y intercept is (0,-9)

For the last problem you have to plug the variables into the equation
1. 3(0) -2y = 24
y = -12
2. 3x - 2(3) = 24
x = 10
3. 3(2) - 2y = 24
y = -9
4. 3(8) - 2y = 24
y = 0
5. 3x - 2(-3) = 24
x = 6

Answer 3

1)X-intercept means it pass the x and therefore the y will be 0.
Thus, we substitute y=0 to the equation
3x + 5y = 2
3x + 5x0 = 2
3x=2
x=1.5
so, the x intercept is 1.5

2)Again, X-intercept means it pass the x and therefore the y will be 0.
Thus, we substitute y=0 to the equation
3x - y = 9
3x - 0 =9
3x = 9
x = 3
so the x intercept is 3

Revesely, y intercept means it pass the y and therefore, the x will be 0
Thus, we substitute x=0 to the equation
3x - y = 9
3x0 - y = 9
-y = 9
y = -9
so the y intercept is -9

3) Since the results must satisfy the equation, so we just put in the numbers into the equation
+ x = 0
3x-2y=24
-2y=24
y = -12

+ y = 3
3x-2y=24
3x - 2x3=24
3x - 6 = 24
3x = 30
x = 10

+ x = 2
3x-2y=24
3x2 - 2y = 24
6 - 2y = 24
-2y = 18
y = 9

+ x = 8
3x - 2y = 24
3x8 - 2y = 24
24 - 2y = 24
-2y = 0
y = 0

+ y = -3
3x - 2y = 24
x - 2x(-3) = 24
x + 6 = 24
x= 18

Good luck!

Answer 4

Question 1) What is the x-intercept of the line 3x + 5y = 2.
For x int, set y = 0 and solve for x
3x + 5(0)=2
x=2/3 so your x int is (2/3,0)

Question 2) find the x-intercept and the y-intercept of the line
3x - y = 9.
for x int y=0, for y int x = 0
xint = 3 y int = -9

Question 3 Put in slope int form
3x - 2y = 24
-2y=-3x+24
y=3/2x-12
(0,12) (10,3)(2,-9)(8,0)(6,-3)

Answer 5

For your first question, think about what is being asked.
At the x intercept, y = 0 (draw a picture).
Put this value (y=0) into the equation and you will get x for the point where y=0 (which is the x intercept).

The same is true for the y intercept - at that point, x will be 0. Put x=0 into equation, get answer for y (draw picture again to be sure).

This explanation should help with question 2. Remeber, where does x=0, y=0?

Question 3 is again simple. When you have x, put it into the equation and solve for y, and vice versa. You have your point (x and y pair).

I hope this helps,

~Rocdoc

Answer 6

x-intercept = value of x when y = 0
y-intercept = value of y when x = 0

1) x-intercept of 3x+5y=2, plug in 0 into y and get 3x = 2 and x = 2/3 ----------- answer = (2/3, 0)

2) x-intercept: 3x=9, x=3
y-intercept: -y=9, y=-9

3) x-0, -2y=24, y=-12
y=3, 3x-2(3)=24, 3x=18, x=6
x=2, 3(2)-2y=24, -2y=-18, y=9
x=8, 3(8)-2y=24, -2y=0, y=0
y=-3, 3x-2(-3) =24, 3x=18, x=6

Answer 7

The x- and y-intercept are both an similar, (0,0). to locate the y-intercept, replace x with 0. y = -2(0)^2 = -2(0) = 0 to locate the x-intercept, replace y with 0. 0 = -2x^2 0 = x^2 0 = x

Answer 8

1)You need to first put it in slope-intercept form:
y=mx+b

Subtract 3x from both sides:
5y=-3x+2

Divide 5 from both sides:
y=-3/5x+2/5

To find the x-intercept, set the equation to 0:
-3/5x+2/5=0
-3/5x=-2/5
(-5/3)x=-5/3(-2/5)
x=2/3
(2/3,0)

2)3x-y=9
Subtract 3x from both sides:
-y=-3x+9

Divide -1 from both sides:
y=3x-9

To find the y-intercept, replace x with 0:
y=3(0)-9
y=-9
(0,-9)

To find the x-intercept, set the equation to 0:
3x-9=0
3x=9
x=3
(3,0)

3)On this equation, all the table is telling you to do is to find the intercepts for each one. Here's some examples:
3(0)-2y=24
-2y=24
y=-12
(0,-12)

3x-2(3)=24
3x-6=24
3x=30
x=10
(10,3)

I hope this helps and good luck with your class!

Answer 9

Question 1
3x + 5y = 2
The question is asking at what point does the line cuts the x axis i.e. the value of x when y = 0
3x = 2
x = 2/3
Required answer is (2/3,0)

Question 2
3x - y = 9

Cuts x axis when y = 0:-
3x = 9
x = 3---------Point (3,0)

Cuts y axis when x = 0:-
-y = 9y
y = -9--------Point (0,- 9)

Question 3
3x - 2y = 24---------Point (0,- 12)

3x - 2y = 24
3x - 6 = 24
3x = 30
x = 10--------------Point (10,3)

3x - 2y = 24
6 - 2y = 24
-2y = 18
y = - 9------------Point (2, - 9)

3x - 2y = 24
24 - 2y = 24
-2y = 0
y = 0--------------Point (8,0)

3x - 2y = 24
3x + 6 = 24
3x = 18
x = 6--------------Point (6, - 3)

Go easy with the graph paper!
Hope this helps.