what is the y-intercept form of (3,0) and (0,1)

The equation of a line in **slope-intercept form** is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Find the slope (m)
To find the slope, use the formula:

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

Given the two points \( (3, 0) \) and \( (0, 1) \):
- \( (x_1, y_1) = (3, 0) \)
- \( (x_2, y_2) = (0, 1) \)

Now, substitute the values into the slope formula:

\[
m = \frac{1 - 0}{0 - 3} = \frac{1}{-3} = -\frac{1}{3}
\]

### Step 2: Find the y-intercept (b)
We know one of the points is the y-intercept, which is \( (0, 1) \), so the y-intercept \( b = 1 \).

### Step 3: Write the equation in slope-intercept form
Now that we have the slope \( m = -\frac{1}{3} \) and the y-intercept \( b = 1 \), we can write the equation of the line:

\[
y = -\frac{1}{3}x + 1
\]

This is the slope-intercept form of the line passing through the points \( (3, 0) \) and \( (0, 1) \).

Would you like more details or have any questions? 

Here are 5 related questions to explore further:

1. How do you convert from slope-intercept form to standard form?
2. What is the slope formula and how is it derived?
3. How do you find the x-intercept of a line given its equation?
4. What is the point-slope form of a line, and when is it useful?
5. How do parallel and perpendicular lines relate to their slopes?

**Tip:** Always check that your equation satisfies the points given by substituting them into the final equation!

Learn how to find the slope-intercept form of a line passing through the points (3,0) and (0,1). This problem involves using the slope formula and finding the y-intercept to write the equation of the line. Suitable for students in Grades 8-10.

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