The equation of a line is given below. \[ -2 x-5 y=-10 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and the \( y \)-intercept of the line given by the equation \[ -2x - 5y = -10, \] we can rearrange this equation into the slope-intercept form, which is \[ y = mx + b, \] where \( m \) is the slope and \( b \) is the \( y \)-intercept. ### Step 1: Rearranging the equation Starting with the original equation: \[ -2x - 5y = -10, \] we can isolate \( y \): 1. Add \( 2x \) to both sides: \[ -5y = 2x - 10. \] 2. Divide every term by \(-5\): \[ y = -\frac{2}{5}x + 2. \] ### Step 2: Identifying the slope and \( y \)-intercept From the equation \( y = -\frac{2}{5}x + 2 \): - The slope \( m \) is \(-\frac{2}{5}\). - The \( y \)-intercept \( b \) is \( 2 \). ### Step 3: Graphing the line 1. **Plot the \( y \)-intercept**: Start by plotting the point \( (0, 2) \) on the graph. 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 \( x \)), you move down 2 units (negative \( y \)). Starting from the \( y \)-intercept \( (0, 2) \): - Move 5 units to the right to \( (5, 2) \). - Move down 2 units to \( (5, 0) \). So, another point on the line is \( (5, 0) \). 3. **Draw the line**: Connect the points \( (0, 2) \) and \( (5, 0) \) with a straight line, extending it in both directions. ### Summary - The slope of the line is \(-\frac{2}{5}\). - The \( y \)-intercept is \( 2 \). - The graph of the line passes through the points \( (0, 2) \) and \( (5, 0) \). You can now graph the line based on these points and the slope.