find y such that (4,y) lies on the line of slope m=6 through (1,5).

To find the value of \( y \) such that the point \((4, y)\) lies on the line with slope \( m = 6 \) that passes through the point \((1, 5)\), we can use the point-slope form of the line equation:

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

### Step 1: Write the Equation of the Line
Given:
- Slope \( m = 6 \)
- Point \((x_1, y_1) = (1, 5)\)

Substituting these into the point-slope form:

\[
y - 5 = 6(x - 1)
\]

### Step 2: Simplify the Equation
Expand and simplify the equation to find \( y \) as a function of \( x \):

\[
y - 5 = 6x - 6
\]

Add 5 to both sides to solve for \( y \):

\[
y = 6x - 1
\]

### Step 3: Substitute \( x = 4 \)
Now, substitute \( x = 4 \) into the equation to find the corresponding \( y \):

\[
y = 6(4) - 1
\]

\[
y = 24 - 1
\]

\[
y = 23
\]

### Final Answer
The value of \( y \) such that the point \((4, y)\) lies on the line is \( y = 23 \).

Would you like more details on this solution, or do you have any other questions?

Here are 5 related questions:
1. How would the equation change if the slope was different?
2. What is the significance of the slope in determining the steepness of a line?
3. How do you find the y-intercept from the equation \( y = 6x - 1 \)?
4. How can you determine if another point lies on this same line?
5. How would you find the equation of a line perpendicular to this one through a given point?

**Tip:** When finding the value of \( y \) for a specific \( x \), always substitute \( x \) directly into the simplified equation of the line.

Learn how to find the value of y such that the point (4, y) lies on a line with slope m = 6 passing through the point (1, 5). This problem involves using the point-slope form of a line equation and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation