Write the​ point-slope form of the line satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation.
Passing through ​(2​,4​) and ​(4​,8​) Type the​ point-slope form of the equation of the line.
  
enter your response here 
​(Simplify your answer. Use integers or fractions for any number in the​ equation.)

To write the equation of a line in point-slope form, we first need to determine the slope \(m\) of the line passing through the two given points \((2, 4)\) and \((4, 8)\).

### Step 1: Calculate the Slope

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the given points:

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

### Step 2: Write the Point-Slope Form

The point-slope form of a line is given by:

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

Using the slope \(m = 2\) and the point \((2, 4)\), the point-slope form of the equation is:

\[
y - 4 = 2(x - 2)
\]

### Step 3: Simplify to Slope-Intercept Form

To convert the equation to slope-intercept form (\(y = mx + b\)), we expand and simplify the equation:

\[
y - 4 = 2x - 4
\]

Adding 4 to both sides:

\[
y = 2x
\]

So, the slope-intercept form of the equation is:

\[
y = 2x
\]

### Summary:
- **Point-Slope Form:** \(y - 4 = 2(x - 2)\)
- **Slope-Intercept Form:** \(y = 2x\)

Would you like any more details or have any questions?

Here are some related questions you might consider:
1. How do you find the midpoint between two points?
2. How do you convert the point-slope form to the standard form of a line?
3. What is the geometric interpretation of the slope in a linear equation?
4. How do you determine if two lines are parallel?
5. What is the relationship between the slopes of perpendicular lines?

**Tip:** Always double-check your calculations when determining the slope, as it affects the entire equation.

Learn how to write the point-slope form of a line passing through the points (2, 4) and (4, 8). Includes step-by-step instructions on calculating the slope, using the point-slope form of the equation, and converting it to the slope-intercept form. Suitable for students in Grades 7-9.

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