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!