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 ​(7​,14​) 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.)
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 equation of the line that passes through the points \((7, 14)\) and \((9, 18)\), we can first determine the slope of the line and then use the point-slope form to express the equation.

### Part 1: Point-Slope Form

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (7, 14)\) and \((x_2, y_2) = (9, 18)\):
\[
m = \frac{18 - 14}{9 - 7} = \frac{4}{2} = 2
\]

2. **Use the point-slope form of the equation**:
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
Using point \((7, 14)\) and the slope \(m = 2\):
\[
y - 14 = 2(x - 7)
\]

This simplifies to:
\[
y - 14 = 2x - 14
\]

So, the point-slope form of the equation of the line is:
\[
\boxed{y - 14 = 2(x - 7)}
\]

### Part 2: Slope-Intercept Form

Now we need to convert the point-slope form to slope-intercept form \(y = mx + b\).

1. **Start with the point-slope form**:
\[
y - 14 = 2(x - 7)
\]

2. **Distribute the slope (2)**:
\[
y - 14 = 2x - 14
\]

3. **Add 14 to both sides to solve for \(y\)**:
\[
y = 2x - 14 + 14
\]
\[
y = 2x
\]

Thus, the slope-intercept form of the equation of the line is:
\[
\boxed{y = 2x}
\]

In summary:
- The point-slope form is \(y - 14 = 2(x - 7)\)
- The slope-intercept form is \(y = 2x\)