Write an equation of the line that passes through the points (0,4) and (2,10)
y=


To find the equation of a line passing through two points, we can use the slope-intercept form of a line equation:

\[
y = mx + b
\]

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

### Step 1: Find the slope \( m \)

The slope \( m \) of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the points \((0, 4)\) and \((2, 10)\):
\[
m = \frac{10 - 4}{2 - 0} = \frac{6}{2} = 3
\]

So, the slope \( m = 3 \).

### Step 2: Substitute into the slope-intercept form

Since the line passes through the point \((0, 4)\), we know the y-intercept \( b \) is 4.

Thus, the equation of the line is:

\[
y = 3x + 4
\]

### Final Answer
\[
y = 3x + 4
\]

Would you like more details on how to derive this equation or any other questions?

---

1. How do you find the slope between any two points?
2. What is the importance of the y-intercept in a line equation?
3. How can we verify that a point lies on a line given by an equation?
4. How would the equation change if the line passed through different points?
5. What other forms of a line equation are there, such as point-slope form?

**Tip:** Always double-check the slope calculation when working with points on a graph.

Write an equation of the line that passes through the points (0,4) and (2,10) y=

Learn how to find the equation of a line passing through the points (0,4) and (2,10). This solution explains the process using the slope formula and slope-intercept form, providing a clear step-by-step approach suitable for students in Grades 8-10.

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