https://file.aiquickdraw.com/mathbot/file/1727883367828tmvg9sen.jpg

The graph shows a line, and the task is to find its equation in slope-intercept form, which is typically written as:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept, where the line crosses the y-axis.

### Step 1: Identify two points on the line
From the image, we can observe two points where the line crosses grid intersections:
1. \((2, 1)\)
2. \((3, 4)\)

### Step 2: Calculate the slope (\(m\))
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substitute the points \((2, 1)\) and \((3, 4)\):

\[
m = \frac{4 - 1}{3 - 2} = \frac{3}{1} = 3
\]

So, the slope \(m = 3\).

### Step 3: Find the y-intercept (\(b\))
To find \(b\), use the slope-intercept form \(y = mx + b\) and substitute one of the points, say \((2, 1)\), and the slope \(m = 3\):

\[
1 = 3(2) + b
\]
\[
1 = 6 + b
\]
\[
b = 1 - 6 = -5
\]

### Final Equation
Now that we have \(m = 3\) and \(b = -5\), the equation of the line is:

\[
y = 3x - 5
\]

Would you like further clarification or details on any part of this process?

---

Here are 5 related questions to deepen your understanding:
1. How would the slope change if the line became horizontal?
2. What does it mean if the slope of a line is negative?
3. Can you derive the equation of a line if given the slope and a point not on the y-axis?
4. How do parallel lines relate to their slopes?
5. How do you find the equation of a line perpendicular to the given line?

**Tip:** When finding the slope, always check that you're using points that clearly intersect the grid for accurate results.

Write the equation of this line in slope-intercept form.

Learn how to find the equation of a line in slope-intercept form with this example problem. Using two points, we calculate the slope (m) and y-intercept (b) to write the equation y = 3x - 5. This problem is ideal 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