The problem in the image is asking for the equation of a line in slope-intercept form, given a point and a slope.

Problem:

You are given:

• A point: $(1, -8)$
• A slope: $m = -6$

You need to write the equation of the line in slope-intercept form: $y = mx + b$ where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

Step-by-Step Solution:

1. Start with the slope-intercept form equation: $y = mx + b$

2. Substitute the given slope, $m = -6$: $y = -6x + b$

3. Use the point $(1, -8)$ to solve for $b$:

   • The point $(x, y) = (1, -8)$ satisfies the equation, so substitute $x = 1$ and $y = -8$: $-8 = -6(1) + b$ $-8 = -6 + b$

4. Solve for $b$: $b = -8 + 6$ $b = -2$

5. Write the final equation: $y = -6x - 2$

Answer:

The equation of the line in slope-intercept form is: $y = -6x - 2$

Do you want further details or have any questions?

Here are 5 related questions:

1. How do you find the equation of a line given two points instead of a point and slope?
2. How can you rewrite this equation in standard form $Ax + By = C$?
3. What is the significance of the slope in the context of a graph?
4. How would you graph the equation $y = -6x - 2$?
5. What happens to the slope-intercept form if the slope $m$ is 0?

Tip: Remember, the slope $m$ represents how steep the line is; a negative slope means the line is slanting downwards as you move from left to right.