To find the x and y intercepts of the equation \(7x + 5y = 100\), we can follow these steps:
-
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 \(\left(\frac{100}{7}, 0\right)\).
-
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 \((0, 20)\).