Here are the answers to the questions from the uploaded image:

1) What is the equation for a line in standard form?

• The standard form of a line is:
  $Ax + By = C$
  where $A$, $B$, and $C$ are integers, and $A$ is usually positive.

How do you find the slope and y-intercept?

• Rearrange the equation into slope-intercept form $y = mx + b$: $y = -\frac{A}{B}x + \frac{C}{B}$ Here:
  • $m = -\frac{A}{B}$ is the slope.
  • $b = \frac{C}{B}$ is the y-intercept.

2) What is the equation for a line in slope-intercept form?

• The slope-intercept form of a line is:
  $y = mx + b$
  where $m$ is the slope, and $b$ is the y-intercept.

How do you find the slope and y-intercept?

• From the equation $y = mx + b$:
  • $m$ is the slope directly.
  • $b$ is the y-coordinate of the point where the line crosses the y-axis.

3) What is the equation for a line in point-slope form?

• The point-slope form of a line is:
  $y - y_1 = m(x - x_1)$
  where $m$ is the slope, and $(x_1, y_1)$ is a given point on the line.

How do you find the slope and a given point?

• $m$ is given directly in the equation.
• The point on the line is $(x_1, y_1)$, which can be identified from the equation.

Would you like more detailed explanations for any of these forms? Here are some related questions to expand on the topic:

1. How can you convert between different forms of a linear equation?
2. Why is the slope-intercept form commonly used in graphing?
3. What are practical examples where the point-slope form is most useful?
4. How do you determine if two lines are parallel or perpendicular using their slopes?
5. What is the geometric interpretation of each form of a line equation?

Tip: Always check the signs carefully when working with the slope and intercept to avoid errors!