Graph the linear function by finding \( x \) - and \( y \)-intercepts. Then write the equation using function notation. \( x-y=-1 \)

To graph the linear function given by the equation \( x - y = -1 \), we can find the \( x \)- and \( y \)-intercepts. ### Step 1: Find the \( x \)-intercept The \( x \)-intercept occurs when \( y = 0 \). We can find it by substituting \( y = 0 \) into the equation: \[ x - 0 = -1 \implies x = -1 \] So, the \( x \)-intercept is at the point \((-1, 0)\). ### Step 2: Find the \( y \)-intercept The \( y \)-intercept occurs when \( x = 0 \). We can find it by substituting \( x = 0 \) into the equation: \[ 0 - y = -1 \implies -y = -1 \implies y = 1 \] So, the \( y \)-intercept is at the point \((0, 1)\). ### Step 3: Plot the intercepts Now we can plot the points \((-1, 0)\) and \((0, 1)\) on a coordinate plane. ### Step 4: Draw the line Draw a straight line through the points \((-1, 0)\) and \((0, 1)\) to represent the linear function. ### Step 5: Write the equation in function notation To express the equation in function notation, we can solve for \( y \): Starting from the original equation: \[ x - y = -1 \] Rearranging gives: \[ -y = -1 - x \] Multiplying through by -1: \[ y = 1 + x \] Thus, in function notation, we can write: \[ f(x) = x + 1 \] ### Summary - The \( x \)-intercept is \((-1, 0)\). - The \( y \)-intercept is \((0, 1)\). - The equation in function notation is \( f(x) = x + 1 \).