Graphing a line by first finding its slope and \( y \)-Intercept The equation of a line is given below. \[ 9 x-3 y=6 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and \( y \)-intercept of the line represented by the equation \(9x - 3y = 6\), we need to rewrite the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. Given equation: \(9x - 3y = 6\) Step 1: Rewrite the equation in slope-intercept form. \[ 9x - 3y = 6 \] \[ -3y = -9x + 6 \] \[ y = 3x - 2 \] Now, we have the equation in slope-intercept form: \(y = 3x - 2\). Step 2: Identify the slope and \(y\)-intercept. From the equation \(y = 3x - 2\): - The slope (\(m\)) is 3. - The \(y\)-intercept (\(b\)) is -2. Therefore, the slope of the line is 3 and the \(y\)-intercept is -2. Step 3: Graph the line using the slope and \(y\)-intercept. The slope of 3 means that for every 1 unit increase in \(x\), \(y\) increases by 3 units. The \(y\)-intercept of -2 means that the line crosses the \(y\)-axis at the point (0, -2). Now, we can plot the line on a graph using the slope and \(y\)-intercept.