Find the slope of the line and sketch the graph. \( \begin{array}{l}2 x+5 y=26\end{array} \)

To find the slope of the line given by the equation \(2x + 5y = 26\), we can rearrange the equation into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Starting with the original equation: \[ 2x + 5y = 26 \] We can isolate \(y\) by following these steps: 1. Subtract \(2x\) from both sides: \[ 5y = -2x + 26 \] 2. Divide every term by \(5\): \[ y = -\frac{2}{5}x + \frac{26}{5} \] Now, we can identify the slope \(m\) and the y-intercept \(b\): - The slope \(m = -\frac{2}{5}\) - The y-intercept \(b = \frac{26}{5}\) ### Sketching the Graph 1. **Plot the y-intercept**: The y-intercept is \(\left(0, \frac{26}{5}\right)\), which is approximately \((0, 5.2)\). 2. **Use the slope to find another point**: The slope \(-\frac{2}{5}\) means that for every 5 units you move to the right (positive x-direction), you move down 2 units (negative y-direction). Starting from the y-intercept \((0, 5.2)\): - Move 5 units to the right: \(0 + 5 = 5\) - Move down 2 units: \(5.2 - 2 = 3.2\) This gives us the point \((5, 3.2)\). 3. **Draw the line**: Plot the points \((0, 5.2)\) and \((5, 3.2)\) on the graph and draw a straight line through them. ### Summary - The slope of the line is \(-\frac{2}{5}\). - The y-intercept is \(\frac{26}{5}\) or approximately \(5.2\). - The line decreases as it moves from left to right due to the negative slope. Here is a rough sketch of the graph: ``` y | | * | * | * | * | * |* |________________ x ``` In this sketch, the asterisks represent points on the line, and the line slopes downwards from left to right.