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.)


Given the points \((2, 4)\) and \((4, 8)\), let's write the equation of the line in point-slope form and then convert it to slope-intercept form.

### Step 1: Find the Slope
The slope \(m\) is calculated using the formula:

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

Substituting the points \((x_1, y_1) = (2, 4)\) and \((x_2, y_2) = (4, 8)\):

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

### Step 2: Write the Point-Slope Form
The point-slope form of a line is:

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

Using the slope \(m = 2\) and the point \((2, 4)\):

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

### Step 3: Simplify to Slope-Intercept Form
To convert this to slope-intercept form (\(y = mx + b\)), expand and simplify:

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

Add 4 to both sides:

\[
y = 2x
\]

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

If you need more details or have questions, feel free to ask!

Here are some related questions you might consider:
1. How can you verify if a point lies on the line given its equation?
2. What is the equation of a line parallel to this one passing through a different point?
3. How would the equation change if one of the points was negative?
4. How do you find the y-intercept directly from two points?
5. What is the equation of the line perpendicular to this one passing through \((2, 4)\)?

**Tip:** When working with fractions or more complex numbers, it's often useful to check your work by substituting the points back into the equation to ensure they satisfy it.

Learn how to write the point-slope and slope-intercept forms of a line passing through points (2, 4) and (4, 8). This problem involves calculating the slope, applying the point-slope formula, and converting it to the slope-intercept form. Suitable for students in Grades 7-9.

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