What is the x and y intercepts?

Question

What is the x and y intercepts? for
2x-3y=9

i'm not 100% sure how to work it out.


also have no idea with this one:

what is the equation of the line parallel to 2y=4x-8 but passing through (1, 5)?

If anyone could help it would be heaps appreciated =D

Answer 1

First Question:

2x - 3y = 9

By definition, the intercept is where the function intersect with the axis. Therefore, the x-intercept is where the function intersect with the x-axis, and y-intercept is where the function intersect with the y-axis. At the same time, the x-axis is a horizontal line which y = 0; and y-axis is a vertical line which x = 0.

Therefore, to find x -intercept, we substitute y with 0 into the equation; and to find y-intercept, we substitute x = 0 into the equation.

x-intercept:

2x = 9

x = 9/2

y-intercept:

-3y = 9

y =-3


Second Question:

Line parallel means slope is the same, so you need to simply the equation into slope-intercept form first.

y = mx +b

m: slope
b: y-intercept

2y = 4x - 8
y = 2x - 4

A parallel line will have a form:

y = 2x - b

In order to find b, we need to substitute the point into the equation:

5 = 2(1) + b

b = 3


Therefore, the equation for a line parallel to 2y =4x - 8 will be:

y = 2x + 3

[Finished typing the whole thing and fixed some mistakes I made]

Answer 2

The standard form for the equation of a line is y=mx+b where m is the slope and b is the y-intercept.

So, let's take the first equation and put it in this form.

2x-3y=9 so, subtract 2x from each side, and you get:
-3y=-2x+9

Now, divide by -3 on both sides, and you get:

y=(2/3)x-3

So, now you know that the y-intercept is -3. (You can tell this by substituting a 0 for x). Now, to get the x-intercept, set y=0 (i.e., that's where the line crosses the x-axis), and solve for x. So,

0=(2/3)x-3 Add 3 to both sides, and you get:
(2/3)x=3 Multiply by 3 on both sides, and you get:

2x=9 Divide by 2 on both sides, and you get:

x=9/2 That's the x-intercept


As for the second question, the first trick is to figure out the slope. All lines with the same slope are parallel.

So, you have 2y=4x-8

Divide by 2 on both sides, and you get:

y=2x-4 Now you know that the slope of the new line has to be 2 by definintion.

Now, all you need is the y-intercept of the new line. Now, to do that, you have to realize that the slope is defined as the change in x/ change in y.

So, you are looking for y in the point (0,y) -i.e., the y-intercept - for the line with slope 2 that goes through point (1,5)

So, the change in x is 1-0. The change in y is 5-y. So,
(5-y)/1 or 5-y is the slope of the line. So, you get:

5-y = 2 Subtract 5 from both sides, and you get:

-y=-3 or y=3

Now, the equation is y=2x+3

Answer 3

The x-intercept as the word suggests, is where the line will cut the x-axis. On the x-axis, the ordinate of the point is 0, so to find x-intercept, substitute y= 0 and solve.

Similarly, the y-intercept is where the line cuts the y-axis, and for that to happen, the x coordinate is 0. So substitute x = 0 to find out.

2)
i) The slope of a line ay= bx + c is given by b/a.
ii) Two lines are parallel if they have the same slope
iii) the equation of a line passing through a point (p,q) is
y-q=m(x-p), where m is the slope.

You now have all the tools to be able to answer your questions, so start.

Answer 4

X intercept is the value of x in equation at y=0. And y-intercept is the value of y in the equation at x=0.

2x-3y=9

x- intercept, let y=0 so x will become x=9/3 this is the x-intercept.

y-intercept, let x=0 so y will become y= -3. This is the y-intercept.

2y=4x-8

The line slope is 4/2 or 2.
Since the unknown line is parallel with the previous line therefore there slope are the same.

Using the equation of the line,

( y-y1)/(x-x1) = slope

x1= 1 , y1=5

Therefore line equation is,

y = 2(x - 1) + 5

Answer 5

2x - 3y = 9

x intercept is the value of x when y = 0

y intercept is the value of y when x = 0

x - intercept

2x - 3(0) = 9

x = 4.5

y - intercept

2(0) - 3y = 9

y = -3

Parallel lines have the same slope

we can solve the slope from the eq. 2y = 4x - 8,

convert to std. eq, y = mx + b, where m = slope of the line

y = 2x -4, therefore, m = 2

solving for the eq. of the 2nd line, using the formula for slope

m = (y - y1)/(x - x1), given pt. is (1, 5)

2 = (y - 5)/(x - 1), simplify

2x - 2 = y - 5

2x - y + 3 = 0

Answer 6

y=mx+b is how you get y-intercept

You're problem would be 3y=2x-9 if you subtracted 3y from both sides, and subtracted 9 from both sides.

Then you get y by it's self by dividing both sides by 3. so you have y=2/3x-3

You're slope is 2/3 and you're y-intercept is -3

I'm having a hard time remembering how you find the x-intercept...

but as for your other question you need to change the problem into y=mx+b again to find the slope.

So you would get y=2x-4 so your slope is 2. I can't remember how to get the last part......

Sorry... I hope I helped some though, to at least get you started

Good luck

Answer 7

for the 2nd : If a line parallel to another line so it must be the slope of the 1st line = the slope of th 2nd line , and to get the slope of line its -(factor of X)/(factor of Y) for ur example the -(factor of X)= -4 and (factor of Y)= -2 How? cause the form of equation should be at that form 4X-2Y-8=0 so the factor of Y= -2 then the slope = (-4)/(-2) = 2 ,which is also the slope of requested line , and from the general form of any line: ( Y - Y1) = ( X - X1)*Slope note:(X1,Y1) = ( 1 , 5 ) .. i mean (X1,Y1) is any point lie on the requested line
so the requested line equation is: (Y-5) = (X-1)* (2)........... I hope that useful for u

Answer 8

to find the x-intercept you make y=0. To find the y-intercepty you make x=0.

Answer 9

Y intercept

2x - 3y = 9

2x - 3y - 2x = - 2x + 9

- 3y = - 2x + 9

- 3y / - 3 = - 2x / - 3 + (9 / - 3)

y = 2/3x - 3

- - - - - - - - - -

x intercept

2x - 3y = 9

2x - 3y + 3y = 3y + 9

2x = 3y + 9

2x / 2 = 3y / 2 + 9/2

x = 3/2y + 9/2

- - - - - - - - - -s-

Answer 10

y = mx + c
2x-3y = 9
3y = 2x-9
y = (2x-9)/3
y = (2/3)x-3
m = slope
m = 2/3
c = y intercept
c = -3

second one forgotten.,need time.., long years back i have done