Question

Write the​ point-slope form of the​ line's equation satisfying the given conditions. Then use the​ point-slope form of the equation to write the​ slope-intercept form of the equation.
Slopeequals5​, passing through ​(5​,4​)
Question content area bottom
Part 1
What is the​ point-slope form of the equation of the​ line?
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)
Part 2
What is the​ slope-intercept form of the equation of the​ line?
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

Answer 1

To find the equations of the line using the given slope and point, we'll start with the point-slope form.

### Part 1: Point-Slope Form

The point-slope form of a line's equation is given by:

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

where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.

Given:
- Slope \(m = 5\)
- Point \((x_1, y_1) = (5, 4)\)

Substituting these values into the point-slope form:

\[
y - 4 = 5(x - 5)
\]

So the point-slope form of the equation is:

\[
y - 4 = 5(x - 5)
\]

### Part 2: Slope-Intercept Form

To convert from point-slope form to slope-intercept form, we need to solve for \(y\):

Starting from:

\[
y - 4 = 5(x - 5)
\]

Distributing the slope on the right side:

\[
y - 4 = 5x - 25
\]

Now, add 4 to both sides to solve for \(y\):

\[
y = 5x - 25 + 4
\]
\[
y = 5x - 21
\]

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

\[
y = 5x - 21
\]

### Summary:
1. **Point-Slope Form**: \(y - 4 = 5(x - 5)\)
2. **Slope-Intercept Form**: \(y = 5x - 21\)