Write an equation for a line passing through the points (-5,-6) and (1,3)

To find the equation of a line passing through two points, we can use the point-slope form of the line equation, which is:

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

Where:
- \((x_1, y_1)\) is one of the points on the line.
- \(m\) is the slope of the line, calculated by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points \((-5, -6)\) and \( (1, 3)\):

1. Calculate the slope \(m\):

\[
m = \frac{3 - (-6)}{1 - (-5)} = \frac{3 + 6}{1 + 5} = \frac{9}{6} = \frac{3}{2}
\]

2. Now, use the point-slope form with the slope \(m = \frac{3}{2}\) and one of the points, say \((1, 3)\):

\[
y - 3 = \frac{3}{2}(x - 1)
\]

3. To express this in slope-intercept form \(y = mx + b\):

Expand and simplify:

\[
y - 3 = \frac{3}{2}x - \frac{3}{2}
\]

\[
y = \frac{3}{2}x - \frac{3}{2} + 3
\]

\[
y = \frac{3}{2}x + \frac{3}{2}
\]

So, the equation of the line is:

\[
y = \frac{3}{2}x + \frac{3}{2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line if given two points?
2. What is the point-slope form of a line?
3. How can you convert the point-slope form to slope-intercept form?
4. What is the significance of the y-intercept in the slope-intercept form?
5. Can you find the equation of a line parallel to the given line that passes through a different point?

**Tip:** Always check your slope calculation first, as it determines the accuracy of the line equation.

Learn how to find the equation of a line passing through the points (-5,-6) and (1,3) using the point-slope form of a line equation. This problem involves calculating slope, applying the point-slope form, and converting to slope-intercept form. 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