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.

$$7x+5(0)=1007x=100x=\frac{100}{7}$$

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

2. Finding the y-intercept:

To find the y-intercept, set $x=0$ in the equation.

$$7(0)+5y=1005y=100y=\frac{100}{5}=20$$

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

Conclusion:

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