What is the equation of the line that passes through the point left parenthesis, minus, 8, comma, minus, 8, right parenthesis(−8,−8) and has a slope of 22?
Answer
Attempt 1 out of 2

The equation of a line can be written in the slope-intercept form:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. To find the equation of the line, we are given:

- A point \( (-8, -8) \)
- A slope \( m = 22 \)

We can substitute these values into the point-slope form of a line equation, which is:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point on the line. Plugging in \( (-8, -8) \) and \( m = 22 \):

\[
y - (-8) = 22(x - (-8))
\]

Simplify the equation:

\[
y + 8 = 22(x + 8)
\]

Now, distribute the \( 22 \) on the right side:

\[
y + 8 = 22x + 176
\]

Subtract \( 8 \) from both sides:

\[
y = 22x + 168
\]

So, the equation of the line is:

\[
y = 22x + 168
\]

Would you like further details on this solution, or do you have any specific questions?

Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the point-slope form of a line, and how does it differ from slope-intercept form?
3. Can you derive the equation of a line parallel to this one passing through a different point?
4. How would the equation change if the slope was negative instead of positive?
5. What is the equation of a vertical line through the point \( (-8, -8) \)?

**Tip:** Always use the point-slope form when given a specific point and slope, as it makes finding the equation easier!

What is the equation of the line that passes through the point (-8, -8) and has a slope of 22?

Find the linear equation of a line passing through the point (-8, -8) with a slope of 22 using the point-slope form and converting it into slope-intercept form. This problem covers key algebra concepts such as slope-intercept and point-slope forms. Suitable for students in Grades 9-10.

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