https://file.aiquickdraw.com/mathbot/file/1729183658953c4fc0qk2.jpg

Let's break down and solve the problems shown in the image step by step:

### 1. First Equation: \( y = -5x + 2 \)

- **Slope**: The equation is already in slope-intercept form \( y = mx + b \), where:
  - \( m \) is the slope.
  - \( b \) is the y-intercept.
  - Here, \( m = -5 \) and \( b = 2 \).

  **Answer**:
  - Slope \( = -5 \)
  - Y-intercept \( = 2 \)

### 2. Second Equation: \( y = -x - 10 \)

- **Slope**: Again, this equation is in slope-intercept form \( y = mx + b \).
  - The slope \( m = -1 \), because \( y = -x \) is the same as \( y = -1x \).
  - The y-intercept \( b = -10 \).

  **Answer**:
  - Slope \( = -1 \)
  - Y-intercept \( = -10 \)

### 3. Write an Equation Using the Points (0, 2) and (7, 7)

To write the equation of the line, we need the slope and y-intercept.

- **Find the Slope**:
  Using the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where:
  - \( (x_1, y_1) = (0, 2) \)
  - \( (x_2, y_2) = (7, 7) \)
  
  \( m = \frac{7 - 2}{7 - 0} = \frac{5}{7} \)

- **Find the Equation**:
  The y-intercept is given by the point \( (0, 2) \), so \( b = 2 \). Using the slope-intercept form \( y = mx + b \):
  - \( y = \frac{5}{7}x + 2 \)

  **Answer**: The equation is \( y = \frac{5}{7}x + 2 \).

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Would you like more details or clarifications on any of the steps? 

Here are some follow-up questions to consider:

1. What is the slope if the equation is written in standard form \( Ax + By = C \)?
2. How do you find the slope between two points if one of the points is negative?
3. What happens to the graph of a line when the slope is increased or decreased?
4. Can you explain how to convert from slope-intercept form to point-slope form?
5. How would the equation change if the y-intercept were negative?

**Tip**: Always remember, the slope represents the "steepness" of the line. A positive slope means the line rises, while a negative slope means the line falls.

1) y = -5x + 2, 2) y = -x - 10, 3) Use the points (0, 2) and (7, 7) to write an equation.

Learn how to solve linear equations, find slopes, and determine the slope-intercept form. The solution includes calculating the slope for the equations y = -5x + 2, y = -x - 10, and using points (0, 2) and (7, 7) to find an equation of a line. Suitable for Grades 7-9.

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