Question

Use the given conditions to write an equation for the line in​ point-slope form and in​ slope-intercept form.  
​x-intercept = negative three fifths
and​ y-intercept = 5
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Part 1
Type the​ point-slope form of the equation of the line.
  
enter your response here
​(Use integers or simplified fractions for any numbers in the​ equation.)

Answer 1

To use the given conditions to write the equation of the line in both point-slope form and slope-intercept form, we first need to identify a few key points based on the intercepts you provided.

1. **X-Intercept:** The x-intercept is \((-3/5, 0)\).
2. **Y-Intercept:** The y-intercept is \((0, 5)\).

Next, let's find the slope (m) of the line using the two intercept points:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - (-3/5)} = \frac{5}{3/5} = 5 \cdot \frac{5}{3} = \frac{25}{3}
\]

Now that we have the slope, we can use either the x-intercept or y-intercept to write the point-slope form of the equation. We'll use the y-intercept (0, 5) for this example.

### Point-Slope Form
The point-slope form of an equation is given by:

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

Substituting the slope \(m = \frac{25}{3}\) and the point \( (0, 5) \):

\[
y - 5 = \frac{25}{3}(x - 0)
\]

This simplifies to:

\[
y - 5 = \frac{25}{3}x
\]

**Final Point-Slope Form:**

\[
y - 5 = \frac{25}{3}x
\]

---

### Slope-Intercept Form
The slope-intercept form of a line is given by:

\[
y = mx + b
\]

Here, \(m\) is the slope and \(b\) is the y-intercept. We already have \(m = \frac{25}{3}\) and \(b = 5\):

\[
y = \frac{25}{3}x + 5
\]

**Final Slope-Intercept Form:**

\[
y = \frac{25}{3}x + 5
\]

### Summary of the Equations
- Point-Slope Form: \(y - 5 = \frac{25}{3}x\)
- Slope-Intercept Form: \(y = \frac{25}{3}x + 5\)