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.