equation of the line?

Question

(0,-3) with a slope of 2/5. find the equation of a line. how on earth do u do this?? my choices are..please exsplain this to me
a] -5x+3y=23
b]-3x+2y=17
c]2x-5y=15
d]-2x+5y=15

Answer 1

(y-y1)=m(x-x1)
y+3=2/5(x-0)
y+3=2/5x
y=2/5x-3
-5(y)=-5(2/5x-3)
-5y=-2x+15
2x-5y=15
The answer is c).

Answer 2

*Make sure you know the slope-intercept formula:

y = mx + b

First: take the point (0, -3), the slope (m) = 2/5 and replace them with the appropriate variable:

- 3 = (2/5)(0) + b
- 3 = 0 + b

Second: find the y-intercept, represented as "b" by keeping it on one side: just disregard zero since it doesn't exist:

- 3 = b; b = - 3

Third: take the slope, y-intercept and place them into the slope-intercept form:

y = (2/5)x - 3

*This is standard form. If your teacher wants it written in the general form, set it to equal zero.

First: get rid of fractions > take the denomintor and multiply it by everything:

5y = 5(2/5)x - 5(3)
5y = 2x - 15

Second: add 15 to both sides:

5y + 15 = 2x - 15 +15
5y + 15 = 2x

Third: subtract 2x from both sides and write it in alpha descending order: Ax + By + C > the leading coefficient can't be negative, just change all the signs:

5y - 2x + 15 = 2x - 2x
5y - 2x + 15 = 0
-2x + 5y + 15 = 0
2x - 5y - 15 = 0

Answer 3

Easy. You know the formula of a line is y=mx+b. (x,y) is ANY point on that line. m is the slope of that line and b is the y intercept. You know 2 of the 3 items, so you can find the 3rd term to find the equation.
the point is (0, -3) and the slope is 2/5. Plug this in:
-3=(2/5)*(0)+b
therefore b=-3
Then, just plug in everything except (x,y)
y=(2/5)x-3
see how I determined the third term by using the two terms given?
ok. now since none of the choices look like our answer, just rearange the answers.
good luck

Answer 4

an easy way around this type of question when you have multiple choice is just to plug in numbers! which of the lines crosses through (0,-3)?

plugging in:
a) -9 = 23
b) -6 = 17
c) 15 = 15
d) -15 = 15

you will find that none of them but c) does, and it saves you a lot of work.

Answer 5

You can use this equation.
(y - y1) = m(x - x1)
where m is the slope
and (x1,y1) is any point within the line.

since the values m and (x1,y1) are given
m = 2/5
(x1,y1) = (0,-3)

We just substitute these to the equation above.
So we get,
y - (-3) = 2/5(x - 0)
y + 3 = 2/5x

we multiply 5 to both sides of the equation to get rid of the fraction part
5y + 15 = 2x

therefor the answer is c
2x - 5y = 15

Answer 6

Start with the basic equation form y = mx + b. You've been given one set of coordinates (x, y), and the slope (m), so you plug those in to find b.

y = mx + b
-3 = (2/5) (0) + b
b = -3

Now you can write it with x and y as variables.

y = 2/5 x -3

Now you can write in in standard form instead of graphing.

y = 2/5 x -3
-2/5 x + y = -3
2/5 x - y = 3
2x - 5y = 15

So the answer is c.

Answer 7

this is easy! when u see questions like these, first try plugging in numbers.
since u kno that the equation of a line is: y = mx + b where m = slope of the line and b = the y-intercept, u can see that your choices are not in this format, so just rearrange the equation to fit it. It'll look like this:
-mx+y = b
then just plug in for m(the slope) x and y. for wichever option when the left-side of the equation equals the right-side, then u know that u've found the right x and y. It'll look like this:

a) -9 = 23 --> wrong!
b) -6 = 17 --> wrong!
c) 15 = 15 --> CORRECT!!!!
d) -15 = 15 --> wrong!

You see? if you practice with more probs like these, you'll become very comfortable since these are anythign BUT hard!

Good luck!

Answer 8

-3 = (2/5)(0) + b
-3 = 0 + b
b = -3

y = (2/5)x - 3
5y = 2x - 15
-2x + 5y = -15

This is the same as saying 2x - 5y = 15

ANS : c.) 2x - 5y = 15

Answer 9

it is choice c
-5y=-2x+15
y=(2/5)+3
slope=2/5
and y intercept is (0,-3)

Answer 10

Go through each equation and solve it for the y-variable.

a) y = (5/3)x+23/3
b) y = x + 17/3
c) y = (2/5)x - 3...DING DING DING DING
d) y = (2/5)x + 3