The equation 10x+3y=90

Question

is in standard form. This form tells us the x and y-intercepts easily.

What are the x and y-intercepts?

(1 point)
Responses

The x-intercept is (10,0) and the y-intercept is at (0,3).
The x-intercept is (10,0) and the y-intercept is at (0,3).

The x-intercept is (3,0) and the y-intercept is at (0,10).
The x-intercept is (3,0) and the y-intercept is at (0,10).

The x-intercept is (9,0) and the y-intercept is at (0,30).
The x-intercept is (9,0) and the y-intercept is at (0,30).

The x-intercept is (1/9,0) and the y-intercept is at (0,1/30).

Answer 1

To find the x-intercept and y-intercept of the equation \(10x + 3y = 90\):

1. Finding the x-intercept:

   • Set \(y = 0\) in the equation: \[ 10x + 3(0) = 90 \quad \Rightarrow \quad 10x = 90 \quad \Rightarrow \quad x = \frac{90}{10} = 9 \]
   • So the x-intercept is \((9, 0)\).

2. Finding the y-intercept:

   • Set \(x = 0\) in the equation: \[ 10(0) + 3y = 90 \quad \Rightarrow \quad 3y = 90 \quad \Rightarrow \quad y = \frac{90}{3} = 30 \]
   • So the y-intercept is \((0, 30)\).

Thus, the x-intercept is \((9, 0)\) and the y-intercept is \((0, 30)\).

The correct response is: The x-intercept is (9,0) and the y-intercept is at (0,30).