Question

Question

The equation 7x + 5y = 100 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 line crosses the x-axis at (20, 0) and crosses the y-axis at (0, 100/7).
The line crosses the x-axis at (20, 0) and crosses the y-axis at (0, 100/7).

The line crosses the x-axis at (100/7, 0) and crosses the y-axis at (0, 20).
The line crosses the x-axis at (100/7, 0) and crosses the y-axis at (0, 20).

The line crosses the x-axis at (7/100, 0) and crosses the y-axis at (0, 1/20).
The line crosses the x-axis at (7/100, 0) and crosses the y-axis at (0, 1/20).

The line crosses the x-axis at (7, 0) and crosses the y-axis at (0, 5).
The line crosses the x-axis at (7, 0) and crosses the y-axis at (0, 5).
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Answer 1

To find the x-intercept and y-intercept of the equation \(7x + 5y = 100\), we can use the following methods:

1. Finding the x-intercept:

To find the x-intercept, set \(y = 0\) in the equation.

\[ 7x + 5(0) = 100 \ 7x = 100 \ x = \frac{100}{7} \]

So, the x-intercept is \(\left(\frac{100}{7}, 0\right)\).

2. Finding the y-intercept:

To find the y-intercept, set \(x = 0\) in the equation.

\[ 7(0) + 5y = 100 \ 5y = 100 \ y = \frac{100}{5} = 20 \]

So, the y-intercept is \((0, 20)\).

Conclusion:

The line crosses the x-axis at \(\left(\frac{100}{7}, 0\right)\) and crosses the y-axis at \((0, 20)\).

Thus, the correct response is: The line crosses the x-axis at \((\frac{100}{7}, 0)\) and crosses the y-axis at \((0, 20)\).