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 ​(8​,16​) and ​(9​,18​)
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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.)

Answer 1

To find the point-slope form of the equation of the line passing through the points \((8, 16)\) and \((9, 18)\), we first need to calculate the slope \(m\) using the formula:

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

Using the points \((x_1, y_1) = (8, 16)\) and \((x_2, y_2) = (9, 18)\):

\[
m = \frac{18 - 16}{9 - 8} = \frac{2}{1} = 2
\]

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

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

We can use the point \((8, 16)\) for \((x_1, y_1)\):

\[
y - 16 = 2(x - 8)
\]

This is the point-slope form of the equation.

### Part 1: Point-Slope Form
Thus, the point-slope form of the line is:

\[
y - 16 = 2(x - 8)
\]

### Part 2: Slope-Intercept Form
Now, let's convert this to slope-intercept form (which is \(y = mx + b\)).

Starting with the point-slope form:

\[
y - 16 = 2(x - 8)
\]

Distributing the 2 on the right side:

\[
y - 16 = 2x - 16
\]

Now, add 16 to both sides:

\[
y = 2x - 16 + 16
\]

This simplifies to:

\[
y = 2x
\]

### Final Answer:
**Point-Slope Form:**
\(y - 16 = 2(x - 8)\)

**Slope-Intercept Form:**
\(y = 2x\)