https://file.aiquickdraw.com/mathbot/file/17290210150002x3cxzx9.jpg

To write the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the two given points: \( (0, 1) \) and \( (4, 2) \).

### Step 1: Calculate the slope
The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 1) \) and \( (4, 2) \):
\[
m = \frac{2 - 1}{4 - 0} = \frac{1}{4}
\]
So, the slope \( m = \frac{1}{4} \).

### Step 2: Identify the y-intercept
From the graph and the given point \( (0, 1) \), the y-intercept \( b \) is clearly \( 1 \).

### Step 3: Write the equation
Now that we have the slope \( m = \frac{1}{4} \) and the y-intercept \( b = 1 \), the equation of the line in slope-intercept form is:
\[
y = \frac{1}{4}x + 1
\]

Would you like more details or further clarification?

Here are five related questions to expand your understanding:
1. How would you find the equation if you were given different points?
2. What does the slope tell you about the direction of the line?
3. How would the equation change if the y-intercept were different?
4. Can the slope be negative? What would that look like on a graph?
5. How can you check if a point lies on a line given its equation?

**Tip:** Always check the y-intercept from the graph or the given points directly; it's the easiest way to get the full equation quickly!

Write an equation in slope-intercept form of the line that passes through the points (0,1) and (4,2).

Learn how to write the equation of a line passing through points (0,1) and (4,2) in slope-intercept form. This problem demonstrates key algebraic concepts like the slope formula and identifying the y-intercept. 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