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?

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

Answer 1

To find the x and y intercepts of the equation \(7x + 5y = 100\), we can follow these steps:

1. **Finding the x-intercept**: To find the x-intercept, set \(y = 0\) in the equation and solve for \(x\).
\[
7x + 5(0) = 100 \implies 7x = 100 \implies x = \frac{100}{7}
\]
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 and solve for \(y\).
\[
7(0) + 5y = 100 \implies 5y = 100 \implies y = \frac{100}{5} = 20
\]
So, the y-intercept is \((0, 20)\).

Thus, the x and y intercepts are \(\left(\frac{100}{7}, 0\right)\) and \((0, 20)\).

From the provided options, the correct one is:
**The line crosses the x-axis at \(\left(\frac{100}{7}, 0\right)\) and crosses the y-axis at \((0, 20)\).**