https://file.aiquickdraw.com/mathbot/file/1726890192432mlf00ye3.jpg

To write the equation of a line in slope-intercept form (\( y = mx + b \)), we need to determine two key components:

1. **Slope** (\( m \)): The slope is found using the formula:

   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \( (x_1, y_1) = (6, -2) \) and \( (x_2, y_2) = (12, 1) \).

2. **Y-intercept** (\( b \)): Once we have the slope, we can use the point-slope form of the equation, \( y - y_1 = m(x - x_1) \), or substitute one of the points and the slope into \( y = mx + b \) to find \( b \).

Let's calculate the slope first:

\[
m = \frac{1 - (-2)}{12 - 6} = \frac{1 + 2}{6} = \frac{3}{6} = \frac{1}{2}
\]

Now, using the point \( (6, -2) \), substitute into the slope-intercept form to find \( b \):

\[
-2 = \frac{1}{2}(6) + b
\]

\[
-2 = 3 + b
\]

\[
b = -5
\]

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

\[
y = \frac{1}{2}x - 5
\]

Would you like further clarification or more details?

Here are 5 related questions for you:
1. How do you find the slope when given two points?
2. What is the point-slope form of a line?
3. How can you graph a line using slope-intercept form?
4. How do you convert point-slope form to slope-intercept form?
5. What is the geometric significance of the y-intercept?

**Tip**: Always double-check that you substitute the correct coordinates when calculating slope and intercepts to avoid errors!

Write an equation in slope-intercept form of the line that passes through (6, -2) and (12, 1).

Learn how to find the equation of a line in slope-intercept form that passes through the points (6, -2) and (12, 1). This solution covers key algebraic concepts such as calculating the slope and determining the y-intercept. Suitable for 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