Let's work through each question based on the photo.

Question 1: Calculate the Slope

1. (a) Given the equation $5y = -2x + 3$, solve for the slope.

   To find the slope, we need to rewrite the equation in the slope-intercept form $y = mx + b$, where $m$ represents the slope.

   • Divide both sides by 5: $y = -\frac{2}{5}x + \frac{3}{5}$
   • The slope $m$ is $-\frac{2}{5}$.

2. (b) Graph interpretation: For the graph shown in part (b), we would find two points on the line and use the slope formula $\frac{y_2 - y_1}{x_2 - x_1}$ to calculate it. Identify points on the line to calculate the slope accurately.

3. (c) Find the slope of a line passing through points $(-3, 2)$ and $(1, 2)$.

   • Use the formula $\frac{y_2 - y_1}{x_2 - x_1}$: $\text{slope} = \frac{2 - 2}{1 + 3} = \frac{0}{4} = 0$
   • The slope is $0$, indicating a horizontal line.

4. (d) Find the slope of a line passing through points $(2, 3)$ and $(1, 2)$.

   • Again, use the slope formula: $\text{slope} = \frac{2 - 3}{1 - 2} = \frac{-1}{-1} = 1$
   • The slope is $1$.

Question 2: Find the Missing Coordinate Using the Given Slope

1. (a) Given points $(q, 9)$ and $(3, 1)$ with a slope of 4, solve for $q$.

   • Set up the equation for slope: $4 = \frac{1 - 9}{3 - q}$
   • Simplify and solve for $q$.

2. (c) Given points $(f, -1)$ and $(7, 3)$ with a slope of $-2$, solve for $f$.

   • Set up the slope equation: $-2 = \frac{3 - (-1)}{7 - f}$
   • Simplify and solve for $f$.

Would you like me to solve each part in full detail?

Follow-Up Questions:

1. What is the process to convert an equation into slope-intercept form?
2. How can you determine the slope from a graph quickly?
3. What are the characteristics of a line with a zero slope?
4. What steps are involved in finding a missing coordinate given the slope?
5. How would you verify your answer for a missing coordinate problem?

Tip:

Remember, in a line equation $y = mx + b$, $m$ is always the slope and gives you the "rise over run" for any two points on the line.