Write a​ slope-intercept equation for a line that passes through 

left parenthesis negative 4 comma 3 right parenthesis(−4,3) 

and 

left parenthesis 2 comma negative 9 right parenthesis(2,−9)

To write the slope-intercept equation for a line passing through the points \((-4, 3)\) and \((2, -9)\), we follow these steps:

### Step 1: Find the Slope (\(m\))
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting the given points \((-4, 3)\) and \((2, -9)\):

\[
m = \frac{-9 - 3}{2 - (-4)} = \frac{-12}{6} = -2
\]

### Step 2: Use the Point-Slope Form
The point-slope form of a line's equation is:

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

We can use either of the given points, but let's use \((-4, 3)\). Substituting the values:

\[
y - 3 = -2(x + 4)
\]

### Step 3: Convert to Slope-Intercept Form
The slope-intercept form is \(y = mx + b\). Distribute and simplify the equation:

\[
y - 3 = -2x - 8
\]

Add 3 to both sides:

\[
y = -2x - 5
\]

So, the slope-intercept equation of the line is:

\[
y = -2x - 5
\]

Do you want more details or have any questions?  

Here are some related questions:
1. How do you find the slope when two points are given?
2. What does the slope of a line represent?
3. How do you convert from point-slope form to slope-intercept form?
4. What is the significance of the y-intercept in the slope-intercept equation?
5. How can you graph the equation of a line using the slope and y-intercept?

**Tip:** Always check your calculations by plugging the points back into the equation to ensure they satisfy the equation.

Learn how to write a slope-intercept equation for a line passing through the points (-4, 3) and (2, -9) with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations, slope calculation, and converting between different forms of linear equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation