Write down an equation in the form

y = mx + b

for the line through the points (1,2) and (7,-1)

To find the equation of the line in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Calculate the slope \( m \)
The slope \( m \) is given by the formula:

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

Substitute the coordinates of the points \( (x_1, y_1) = (1, 2) \) and \( (x_2, y_2) = (7, -1) \):

\[
m = \frac{-1 - 2}{7 - 1} = \frac{-3}{6} = -\frac{1}{2}
\]

### Step 2: Use the point-slope form to find the equation
The equation of the line can be written using one of the points, say \( (1, 2) \):

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

Substitute \( m = -\frac{1}{2} \) and \( (x_1, y_1) = (1, 2) \):

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

### Step 3: Simplify to get the equation in \( y = mx + b \) form

Expand and simplify the equation:

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

Add 2 to both sides:

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

Thus, the equation of the line is:

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

Would you like more details or have any questions?

### Related Questions:
1. How do you determine the y-intercept directly from a graph?
2. What is the geometric interpretation of the slope?
3. How can you find the equation of a line given the slope and one point?
4. What does it mean if the slope of a line is zero?
5. How would you find the equation of a line parallel to another given line?

**Tip:** When finding the slope between two points, it's important to carefully subtract the coordinates in the correct order to avoid errors.

Write down an equation in the form y = mx + b for the line through the points (1,2) and (7,-1).

Discover how to find the equation of a line in the form y = mx + b passing through the points (1,2) and (7,-1). This problem involves key algebraic concepts such as calculating the slope and using the point-slope form. Perfect 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