Write a​ slope-intercept equation for a line that passes through left parenthesis 0 comma negative 7 right parenthesis and left parenthesis 4 comma negative 4 right parenthesis.
Question content area bottom
Part 1
The slope of the given line is mequals
  
enter your response here.
​(Simplify your answer. Type an integer or a simplified​ fraction.)
Part 2
The​ slope-intercept equation for the line is 
  
enter your response here.
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

To solve this problem, we will follow two steps:

### Part 1: Find the Slope
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

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

The given points are \( (0, -7) \) and \( (4, -4) \).

Substitute these values into the slope formula:

\[
m = \frac{-4 - (-7)}{4 - 0} = \frac{-4 + 7}{4} = \frac{3}{4}
\]

So, the slope is \( m = \frac{3}{4} \).

### Part 2: Write the Slope-Intercept Equation
The slope-intercept form of a line is:

\[
y = mx + b
\]

We already know the slope \( m = \frac{3}{4} \), so we need to find the \( y \)-intercept \( b \). Since the line passes through \( (0, -7) \), we can use this point to find \( b \).

Substitute \( x = 0 \), \( y = -7 \), and \( m = \frac{3}{4} \) into the equation \( y = mx + b \):

\[
-7 = \frac{3}{4}(0) + b
\]

\[
b = -7
\]

Now we have both \( m = \frac{3}{4} \) and \( b = -7 \), so the equation of the line is:

\[
y = \frac{3}{4}x - 7
\]

### Final Answer:
- **Slope:** \( \frac{3}{4} \)
- **Slope-Intercept Equation:** \( y = \frac{3}{4}x - 7 \)

Would you like any additional explanations or details?

---

Here are five related questions to explore:
1. How do you find the slope if given only one point and the slope value?
2. What does the slope represent in a real-world context?
3. How do you convert the slope-intercept form to standard form?
4. What is the effect of changing the slope on the steepness of the line?
5. How do you graph a line using the slope-intercept equation?

**Tip:** Always start with the slope formula when working with two points. It's essential for finding the slope quickly!

Write a slope-intercept equation for a line that passes through (0, -7) and (4, -4). Part 1: The slope of the given line is __. (Simplify your answer.) Part 2: The slope-intercept equation for the line is __. (Simplify your answer.)

Learn how to find the slope and write the slope-intercept equation for a line passing through the points (0, -7) and (4, -4). This problem covers key algebraic concepts such as finding the slope using two points and writing linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation