a. Rewrite the given equation \( x+3 y-3=0 \) slope-intercept form. b. Give the slope and \( y \)-intercept. c. Use the slope and \( y \)-intercept to graph the linear function.

To convert the equation \( x + 3y - 3 = 0 \) into slope-intercept form, you need to solve for \( y \). Start by isolating \( y \): 1. Rearrange the equation: \[ 3y = -x + 3 \] 2. Divide by 3: \[ y = -\frac{1}{3}x + 1 \] Now, the equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. The slope (\( m \)) of the equation is \(-\frac{1}{3}\), and the \( y \)-intercept (\( b \)) is \( 1\). This means the line crosses the \( y \)-axis at the point \( (0, 1) \) and for every step of 1 unit you move to the right along the \( x \)-axis, you'll move \(\frac{1}{3}\) units down corresponding to the negative slope. To graph the linear function, start at the \( y \)-intercept point \( (0, 1) \). From there, use the slope: for every 3 units you move to the right (along the \( x \)-axis), move 1 unit down (along the \( y \)-axis) to plot the next point. Mark points along this trend and draw a straight line through them, extending it in both directions to represent the full linear relationship. Don't forget to label your axes!