Tutorial Exercise Find the \( x \) - and \( y \)-intercepts and graph. \[ 2 x+y=9 \] Step 1 To find the \( x \)-intercept, let \( y=0 \). Substituting this value of \( y \) into the equation, we have the following. \[ 2 x+\square=9 \] Solve for \( x \). \[ \begin{aligned} 2 x & =9 \\ x & =\frac{\square}{2} \end{aligned} \] The \( x \)-intercept is therefore \( (x, y)=( \) \( \square \) \( ) \)

Let's follow the steps to find the \( x \)- and \( y \)-intercepts of the equation \( 2x + y = 9 \). ### Step 1: Finding the \( x \)-intercept To find the \( x \)-intercept, we set \( y = 0 \) and substitute this value into the equation: \[ 2x + 0 = 9 \] This simplifies to: \[ 2x = 9 \] Now, we solve for \( x \): \[ x = \frac{9}{2} \] Thus, the \( x \)-intercept is: \[ (x, y) = \left( \frac{9}{2}, 0 \right) \] ### Step 2: Finding the \( y \)-intercept Next, we find the \( y \)-intercept by setting \( x = 0 \) and substituting this value into the equation: \[ 2(0) + y = 9 \] This simplifies to: \[ y = 9 \] Thus, the \( y \)-intercept is: \[ (x, y) = (0, 9) \] ### Summary of Intercepts - The \( x \)-intercept is \( \left( \frac{9}{2}, 0 \right) \). - The \( y \)-intercept is \( (0, 9) \). ### Step 3: Graphing the Equation To graph the equation \( 2x + y = 9 \), we can plot the intercepts we found: 1. Plot the point \( \left( \frac{9}{2}, 0 \right) \) which is \( (4.5, 0) \). 2. Plot the point \( (0, 9) \). Next, we draw a straight line through these two points, which represents the equation \( 2x + y = 9 \). ### Final Graph The graph will show a line that crosses the \( x \)-axis at \( (4.5, 0) \) and the \( y \)-axis at \( (0, 9) \). If you need a visual representation of the graph, please let me know!