a. Rewrite the given equation \( 5 x+7 y-35=0 \) slope-intercept form. b. Give the slope and \( y \)-intercept. c. Use the slope and \( y \)-intercept to graph the linear function. a. The slope-intercept form of the equation is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Sure, let's work through each part of the problem step by step. ### **a. Rewrite the equation in slope-intercept form.** **Given Equation:** \[ 5x + 7y - 35 = 0 \] **Slope-Intercept Form:** The slope-intercept form of a linear equation is: \[ y = mx + b \] where: - \( m \) is the slope - \( b \) is the y-intercept **Steps to Rewrite:** 1. **Isolate the \( y \)-term:** \[ 7y = -5x + 35 \] 2. **Solve for \( y \):** \[ y = \frac{-5}{7}x + 5 \] **Final Slope-Intercept Form:** \[ y = -\frac{5}{7}x + 5 \] --- ### **b. Identify the slope and \( y \)-intercept.** From the slope-intercept form: \[ y = -\frac{5}{7}x + 5 \] - **Slope (\( m \))**: \[ m = -\frac{5}{7} \] - **\( y \)-intercept (\( b \))**: \[ b = 5 \] This means the line crosses the \( y \)-axis at the point \( (0, 5) \). --- ### **c. Graph the linear function using the slope and \( y \)-intercept.** **Steps to Graph:** 1. **Plot the \( y \)-intercept:** - Start by plotting the point \( (0, 5) \) on the graph. 2. **Use the slope to find another point:** - The slope \( m = -\frac{5}{7} \) can be interpreted as "rise over run." - **Rise:** -5 (since the slope is negative, move down) - **Run:** 7 (move to the right) Starting from \( (0, 5) \): - Move right 7 units to \( x = 7 \). - Move down 5 units to \( y = 0 \). - Plot the second point at \( (7, 0) \). 3. **Draw the line:** - Connect the two points \( (0, 5) \) and \( (7, 0) \) with a straight line. - Extend the line across the graph in both directions. **Graph Illustration:** ``` y | 5 | * (0,5) | 4 | | 3 | | 2 | | 1 | | 0 |-------------------------- x 0 7 ``` - The asterisk (*) represents the \( y \)-intercept at \( (0, 5) \). - The point at \( (7, 0) \) is also plotted. - Draw a straight line through these points to represent the linear function \( y = -\frac{5}{7}x + 5 \). --- This completes all parts of the problem. You can use graphing paper or a graphing tool to visualize the line accurately.