The equation 10x+3y=90 is in standard form. This form tells us the x and y-intercepts easily.

Question

What are the x and y-intercepts?

The x-intercept is (9,0), and the y-intercept is (0,30)
The x-intercept is (3,0), and the y-intercept is (0,10)
The x-intercept is (10,0) and the y-intercept is (0,3)
The x-intercept is (1/9,0) and the y-intercept is (0,1/30)

Answer 1

To find the x-intercept and y-intercept of the equation \(10x + 3y = 90\), you can use the following methods:

1. X-intercept: Set \(y = 0\) in the equation and solve for \(x\). \[ 10x + 3(0) = 90 \implies 10x = 90 \implies x = \frac{90}{10} = 9 \] Thus, the x-intercept is \((9, 0)\).

2. Y-intercept: Set \(x = 0\) in the equation and solve for \(y\). \[ 10(0) + 3y = 90 \implies 3y = 90 \implies y = \frac{90}{3} = 30 \] Thus, the y-intercept is \((0, 30)\).

Putting it all together, the x-intercept is \((9, 0)\) and the y-intercept is \((0, 30)\).

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