Which of the following coordinates are intercepts of the linear relation

2x- 3y + 30 = 0 ?

I. (0 , 10)
II.(0 , 2/3)
III.(-10 , 0)
IV.(-15, 0)

A. I only
B. I and IV only
C. II and III only
D. II and IV only

This was what I was trying to do:

2(0)-3(10) + 30 = 0
-30y +30 = 0
subtract 30 frm both sides

-30y/-30y = -30/-30

= 0

Im utterly confused.

2x- 3y + 30 = 0 ?

to find x and y intercepts, put equation in the form
ax + by = c
x intercept = (c/a, 0)
y intercept = (0, c/b)

to find x-intercept, y = 0
2x - 3(0) = -30
2x = -30
x = -15
x intercept = (c/a, 0)
x intercept = (-15, 0)

to find y-intercept, x = 0
2(0) - 3y = -30
-3y = -30
y = 10
y intercept = (0, c/b)
y intercept = (0, 10)

B. I, IV

do you understand?

it would be easier to actually find the intercepts, rather than testing the answers

2x - 3y = -30

here is an easy way:
to let x=0, put your "pinkie" over the x term, what do you see ?
In your head you should be able to solve -3y=-30
or y = 10
to let y=0, put your "pinkie over the y term, what do you see?
can you in your head solve 2x = -30 to get
x = -15

so my intercepts are (0,10) and (-15,0)
do we see those?

Oh that makes sense now. thank you both helper and Reiny so much =]

To find the intercepts of the linear relation 2x - 3y + 30 = 0, you need to substitute each pair of coordinates into the equation and check if it satisfies the equation.

Let's go through each option one by one:

I. (0, 10)
Substituting the values into the equation, we get:
2(0) - 3(10) + 30 = -30 + 30 = 0
Since the equation is satisfied, (0, 10) is an intercept.

II. (0, 2/3)
Substituting the values into the equation, we get:
2(0) - 3(2/3) + 30 = 0 - 2 + 30 = 28
The equation is not satisfied, so (0, 2/3) is not an intercept.

III. (-10, 0)
Substituting the values into the equation, we get:
2(-10) - 3(0) + 30 = -20 + 30 = 10
The equation is not satisfied, so (-10, 0) is not an intercept.

IV. (-15, 0)
Substituting the values into the equation, we get:
2(-15) - 3(0) + 30 = -30 + 30 = 0
Since the equation is satisfied, (-15, 0) is an intercept.

From the calculations, we can conclude that the intercepts of the linear relation are (0, 10) and (-15, 0). Thus, the correct answer is B. I and IV only.