Use point-slope form to write the equation of a line that passes through the point left parenthesis, 16, comma, minus, 1, right parenthesis(16,−1) with slope 33.


The **point-slope form** of a line's equation is given by:

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

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

Given:
- \( (x_1, y_1) = (16, -1) \),
- \( m = 33 \),

Substitute the values into the formula:

\[
y - (-1) = 33(x - 16)
\]

Simplifying:

\[
y + 1 = 33(x - 16)
\]

Now distribute the 33 on the right side:

\[
y + 1 = 33x - 528
\]

Finally, subtract 1 from both sides to solve for \( y \):

\[
y = 33x - 529
\]

So, the equation of the line is:

\[
y = 33x - 529
\]

Do you want more details or have any questions?

Here are some related questions:
1. How can we convert this equation into slope-intercept form?
2. What is the general form of the equation of a line?
3. How would you graph this line using the point and slope?
4. Can you find the x-intercept of this line?
5. How does point-slope form compare to the standard form?

**Tip:** The point-slope form is useful for writing the equation of a line quickly when you know a point and the slope.

Use point-slope form to write the equation of a line that passes through the point (16,−1) with slope 33.

Learn how to write the equation of a line using point-slope form. This example involves the point (16, -1) and a slope of 33, demonstrating key algebraic concepts like the point-slope formula. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation