What is the equation of the line that passes through the point left parenthesis, 8, comma, 6, right parenthesis(8,6) and has a slope of one quarter 
4
1
​
 ?

The equation of a line in slope-intercept form is given by:

\[
y = mx + b
\]

where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

You're given:
- Slope \( m = \frac{1}{4} \),
- A point on the line \( (8, 6) \).

To find the equation of the line, we can use the point-slope form of the equation:

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

where \( (x_1, y_1) \) is the given point. Substituting the values:

\[
y - 6 = \frac{1}{4}(x - 8)
\]

Now, simplify the equation:

\[
y - 6 = \frac{1}{4}x - 2
\]

Add 6 to both sides to solve for \( y \):

\[
y = \frac{1}{4}x + 4
\]

Thus, the equation of the line is:

\[
y = \frac{1}{4}x + 4
\]

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How do you convert from point-slope form to slope-intercept form?
2. What is the y-intercept of the line \( y = \frac{1}{4}x + 4 \)?
3. How can you determine the x-intercept of this line?
4. How do you find the slope of a line between two points?
5. What does the slope \( \frac{1}{4} \) tell you about the steepness of the line?

**Tip:** The slope \( \frac{1}{4} \) indicates that for every 4 units you move horizontally (to the right), the line moves up by 1 unit vertically!

What is the equation of the line that passes through the point (8, 6) and has a slope of 1/4?

Learn how to find the equation of a line that passes through the point (8, 6) and has a slope of 1/4. This detailed explanation covers key algebraic concepts, including the use of point-slope and slope-intercept forms. 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