Find the y intercept of the line passing through the points (-1,3) and (4,6)

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.

Find the y intercept of the line passing through the points (-1,3) and (4,6).

Learn how to find the y-intercept of a line passing through the points (-1, 3) and (4, 6) using the slope formula and point-slope form. This problem covers core algebraic concepts and is suitable for students in Grades 8-10.

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