find the equation of a line that goes through the following points: (0,2) and (4,8)

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

\[
y = mx + b
\]

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

### Step 1: Calculate the slope (\( m \))
The slope formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Using the points \( (0, 2) \) and \( (4, 8) \):

\[
m = \frac{8 - 2}{4 - 0} = \frac{6}{4} = \frac{3}{2}
\]

### Step 2: Use the point-slope form to find the equation
We can use the point-slope form of a line equation:

\[
y - y_1 = m(x - x_1)
\]

Substitute one of the points, say \( (0, 2) \), and the slope \( m = \frac{3}{2} \):

\[
y - 2 = \frac{3}{2}(x - 0)
\]

Simplify:

\[
y - 2 = \frac{3}{2}x
\]

Now, solve for \( y \):

\[
y = \frac{3}{2}x + 2
\]

### Final Equation:
The equation of the line is:

\[
y = \frac{3}{2}x + 2
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might find useful:
1. How do you find the slope between any two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you convert from point-slope form to slope-intercept form?
4. How do you determine if a point lies on a line given its equation?
5. What happens to the line if the slope is 0?

**Tip:** The y-intercept is always where the line crosses the y-axis, so if you have the point \( (0, b) \), then \( b \) is the y-intercept directly!

Learn how to find the equation of a line that passes through the points (0,2) and (4,8). This step-by-step solution covers key algebraic concepts like slope calculation and converting between point-slope and slope-intercept forms. Suitable for students in Grades 8-10.

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