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!