Use point-slope form to write the equation of a line that passes through the point left parenthesis, minus, 4, comma, 8, right parenthesis(−4,8) with slope 1

To write the equation of a line using the point-slope form, we use the following formula:

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

Where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is a point on the line.

In this case:
- The slope \( m = 1 \),
- The point is \( (-4, 8) \).

Substitute these values into the formula:

\[
y - 8 = 1(x - (-4))
\]

Simplify:

\[
y - 8 = 1(x + 4)
\]

Now, distribute the slope \( 1 \) on the right-hand side:

\[
y - 8 = x + 4
\]

Finally, add 8 to both sides to solve for \( y \):

\[
y = x + 12
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = x + 12
\]

Would you like a more detailed breakdown, or do you have any questions?

Here are 5 related questions:
1. How can you convert point-slope form to slope-intercept form?
2. What would the equation be if the slope was negative instead of positive?
3. Can you write the equation of a line through \( (-4, 8) \) with a slope of \( 2 \)?
4. What is the equation of a line parallel to \( y = x + 12 \) through another point?
5. How can you determine the slope of a line if you're given two points?

**Tip:** When writing equations, always make sure to simplify step by step to avoid errors.

Use point-slope form to write the equation of a line that passes through the point (−4,8) with slope 1.

Learn how to write the equation of a line using point-slope form that passes through the point (-4, 8) with a slope of 1. This problem involves algebraic concepts, including point-slope and slope-intercept forms, and is ideal for students in Grades 8-10.

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