Questions: Question 9, 2.1.19 Part 1 of 2 Without sketching the graph, find the x-intercepts and y-intercepts of the graph of the equation. 7x-5y=105 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is/are ]. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts.

Solution Steps

To find the x-intercepts and y-intercepts of the equation \(7x - 5y = 105\), we need to follow these steps:

1. Find the x-intercept: Set \(y = 0\) in the equation and solve for \(x\).
2. Find the y-intercept: Set \(x = 0\) in the equation and solve for \(y\).

To find the \(x\)-intercept, we set \(y = 0\) in the equation \(7x - 5y = 105\) and solve for \(x\): \[ 7x - 5(0) = 105 \implies 7x = 105 \implies x = \frac{105}{7} = 15 \] Thus, the \(x\)-intercept is \(x = 15\).

To find the \(y\)-intercept, we set \(x = 0\) in the equation \(7x - 5y = 105\) and solve for \(y\): \[ 7(0) - 5y = 105 \implies -5y = 105 \implies y = \frac{105}{-5} = -21 \] Thus, the \(y\)-intercept is \(y = -21\).

Final Answer