Question

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 ​(6​,12​) and ​(8​,16​)
Question content area bottom
Part 1
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.)
Part 2
Type the​ slope-intercept form of the equation of the line.
  
enter your response here
​(Simplify your answer. Use integers or fractions for any number in the​ equation.)

Answer 1

To find the point-slope form of the line that passes through the points \( (6, 12) \) and \( (8, 16) \), we first need to calculate the slope of the line using the formula:

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

Let's assign \( (x_1, y_1) = (6, 12) \) and \( (x_2, y_2) = (8, 16) \):

\[
m = \frac{16 - 12}{8 - 6} = \frac{4}{2} = 2
\]

Now that we have the slope \( m = 2 \), we can use the point-slope form of the equation of a line, which is given by:

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

Using the point \( (6, 12) \):

\[
y - 12 = 2(x - 6)
\]

This is the point-slope form.

### Part 1
The point-slope form of the equation of the line is:

\[
y - 12 = 2(x - 6)
\]

### Part 2
Now, we will convert the point-slope form into the slope-intercept form \( y = mx + b \).

Starting with the point-slope equation:

\[
y - 12 = 2(x - 6)
\]

Distributing the \( 2 \):

\[
y - 12 = 2x - 12
\]

Now, add \( 12 \) to both sides:

\[
y = 2x - 12 + 12
\]

This simplifies to:

\[
y = 2x
\]

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

\[
y = 2x
\]

### Summary of Answers
Part 1:
\[
y - 12 = 2(x - 6)
\]

Part 2:
\[
y = 2x
\]