Write an equation (a) in standard form and (b) in slope-intercept form for the line described. through (5,7), parallel to y = - 9 (a) The equation of the line in standard form is (Type your answer in standard form.)

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solve for (a) and (b)

### Problem Description:
Write an equation in two forms: standard form (a) and slope-intercept form (b) for the line described.

**Given:**
- The line passes through the point (5,7).
- The line is parallel to the line given by y = -9.

### Tasks:
1. **(a) The equation of the line in standard form:**
   - Provide the equation in standard form.
   - Input your answer in the provided text box in standard form.

2. **(b) Convert the same equation into slope-intercept form:**
   - Provide the equation in slope-intercept form.

### Step-by-Step Solution:
#### 1. Understanding the problem:
- Since the line is parallel to y = -9, it has the same slope. This line is a horizontal line where y always equals -9, regardless of the value of x.
- Therefore, any line parallel to y = -9 will also be a horizontal line with the same slope (slope = 0) but passing through a different y-coordinate.

#### 2. Finding the equations:
- To find the equation of the line passing through the point (5, 7) and parallel to y = -9, we notice that it's a horizontal line where y = 7 for all x-values.

**(a) Standard Form:**
- For a horizontal line, the standard form is simply y = [constant].
- Here, y = 7. In standard form, this can be written as:
   \[ \boxed{0x + 1y = 7} \]

**(b) Slope-Intercept Form:**
- The given form of the line y = 7 is already in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). In this case, the slope (m) is 0, and the intercept (b) is 7.
   \[ \boxed{y = 7} \]
Transcribed Image Text:### Problem Description: Write an equation in two forms: standard form (a) and slope-intercept form (b) for the line described. **Given:** - The line passes through the point (5,7). - The line is parallel to the line given by y = -9. ### Tasks: 1. **(a) The equation of the line in standard form:** - Provide the equation in standard form. - Input your answer in the provided text box in standard form. 2. **(b) Convert the same equation into slope-intercept form:** - Provide the equation in slope-intercept form. ### Step-by-Step Solution: #### 1. Understanding the problem: - Since the line is parallel to y = -9, it has the same slope. This line is a horizontal line where y always equals -9, regardless of the value of x. - Therefore, any line parallel to y = -9 will also be a horizontal line with the same slope (slope = 0) but passing through a different y-coordinate. #### 2. Finding the equations: - To find the equation of the line passing through the point (5, 7) and parallel to y = -9, we notice that it's a horizontal line where y = 7 for all x-values. **(a) Standard Form:** - For a horizontal line, the standard form is simply y = [constant]. - Here, y = 7. In standard form, this can be written as: \[ \boxed{0x + 1y = 7} \] **(b) Slope-Intercept Form:** - The given form of the line y = 7 is already in slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept). In this case, the slope (m) is 0, and the intercept (b) is 7. \[ \boxed{y = 7} \]
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