Let's break down the questions from your image:

1. Question 1: Find the equation of the line that cuts the y-axis at $y = -9$ and whose slope is $\frac{1}{7}$.

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

   Given:

   • The slope $m = \frac{1}{7}$
   • The y-intercept $b = -9$

   Therefore, the equation of the line will be: $y = \frac{1}{7}x - 9$

2. Question 2: Find the equation of the line $u$ that passes through the point $(-2, 8)$ and whose slope is $1$.

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

   Given:

   • The point $(-2, 8)$
   • The slope $m = 1$

   Substituting into the point-slope form: $y - 8 = 1(x + 2)$ Simplifying: $y - 8 = x + 2$ $y = x + 10$

Would you like any further clarifications on these? Or do you have questions about other problems from the image?

Additional Related Questions:

1. How would you rewrite a line equation in standard form $Ax + By = C$?
2. What are the steps for finding the equation of a line using two points?
3. How can you calculate the slope of a line given two points?
4. What is the difference between slope-intercept and point-slope form?
5. How do you find the y-intercept of a line from its equation?

Tip:

Remember that when using the point-slope form, the point $(x_1, y_1)$ can be any point on the line, not necessarily where it crosses the y-axis.