To find the y-intercept of the line passing through the points $(-1, 3)$ and $(4, 6)$, we follow these steps:

Step 1: Find the slope (m) of the line.

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points $(-1, 3)$ and $(4, 6)$: $m = \frac{6 - 3}{4 - (-1)} = \frac{3}{5} = 0.6$

Step 2: Use the point-slope form of the line equation.

The point-slope form is: $y - y_1 = m(x - x_1)$ Using the point $(-1, 3)$ and the slope $m = 0.6$: $y - 3 = 0.6(x - (-1))$ $y - 3 = 0.6(x + 1)$ $y - 3 = 0.6x + 0.6$ $y = 0.6x + 3.6$

Step 3: Identify the y-intercept.

The y-intercept is the value of $y$ when $x = 0$. From the equation $y = 0.6x + 3.6$, we can see that the y-intercept is: $y = 3.6$

Thus, the y-intercept of the line is $3.6$.

Would you like more details on any step or have any further questions?

Related Questions:

1. How do you find the x-intercept of a line given two points?
2. What is the general form of a linear equation, and how do you convert between forms?
3. How would you find the equation of a line parallel to this one?
4. How does the slope affect the steepness of a line?
5. How do you find the midpoint between two points on a line?

Tip:

Always use the point-slope form when given two points, as it helps derive the equation of the line directly.