a. Put the equation in slope-intercept form. b. Identify the slope and the \( y \)-intercept. c. Use the slope and \( y \)-intercept to graph the line. \( 5 x+6 y=30 \) a. The slope-intercept form of the equation is (Type your answer in slope-intercept form. Use fitegers or fractions for any numbers in the equation. Simplify your answer.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is A.

First, to convert the equation \( 5x + 6y = 30 \) to slope-intercept form, we need to isolate \( y \). Start by subtracting \( 5x \) from both sides: \[ 6y = -5x + 30 \] Next, divide every term by 6: \[ y = -\frac{5}{6}x + 5 \] So, the slope-intercept form is \( y = -\frac{5}{6}x + 5 \). For the second part, the slope is \( -\frac{5}{6} \) (Choice A), and the \( y \)-intercept is \( 5 \) (again, Choice A). Take a moment to imagine graphing this line! Start at the \( y \)-intercept of \( 5 \) on the \( y \)-axis. From there, use the slope of \( -\frac{5}{6} \) which means you go down 5 units and over 6 units to the right to find another point on the line. Connect those dots, and voila! You've graphed a line that descends gently—like a fun slide at the playground! Understanding slope and intercepts is like being a treasure map expert: you're pinpointing where to start and how to move through the graphing jungle! Knowing how to manipulate equations can unlock the wonders of not just simple line graphs but also more complex relationships.