Write an equation of a line in slope intercept form that passes through the points (0,1) and (3,4).  If needed leave slope and y-intercept as an improper fraction and no spaces in your answer.  Make sure your answer is an equation.

To write the equation of a line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:

### Step 1: Find the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, 1) \) and \( (3, 4) \):
\[
m = \frac{4 - 1}{3 - 0} = \frac{3}{3} = 1
\]

### Step 2: Identify the y-intercept \( b \)
Since one of the points is \( (0, 1) \), this point is the y-intercept. So, \( b = 1 \).

### Step 3: Write the equation
Now that we have the slope \( m = 1 \) and y-intercept \( b = 1 \), the equation of the line is:
\[
y = 1x + 1
\]
or simply:
\[
y = x + 1
\]

### Final Answer:
\[
y = x + 1
\]

Would you like further explanation on any part of this?

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1. How would you write an equation if given only a point and a slope?
2. What if the line was vertical—how would the equation look?
3. How can you convert point-slope form to slope-intercept form?
4. How would the equation change if the slope were negative?
5. What if the y-intercept was a fraction—how would you express it?

**Tip:** Remember, any time a line passes through the y-axis at \( x = 0 \), that point gives you the y-intercept directly.

Write an equation of a line in slope intercept form that passes through the points (0,1) and (3,4). If needed leave slope and y-intercept as an improper fraction and no spaces in your answer. Make sure your answer is an equation.

Learn to write the equation of a line in slope-intercept form that passes through the points (0,1) and (3,4). This problem covers algebraic concepts like slope calculation and y-intercept identification, ideal for Grades 8-10 students.

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