What is an equation of the line that passes through the points left parenthesis, minus, 4, comma, 6, right parenthesis(−4,6) and left parenthesis, minus, 2, comma, 0, right parenthesis(−2,0)?
Answer
Attempt 1 out of 2

To find the equation of the line passing through the points \((-4,6)\) and \((-2,0)\), follow these steps:

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

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

Substituting the given points \((-4,6)\) and \((-2,0)\):

\[
m = \frac{0 - 6}{-2 - (-4)}
\]

\[
m = \frac{-6}{-2} = 3
\]

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

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

Using point \((-4,6)\) and slope \( m = 3 \):

\[
y - 6 = 3(x + 4)
\]

### **Step 3: Convert to Slope-Intercept Form**
Distribute the 3:

\[
y - 6 = 3x + 12
\]

Add 6 to both sides:

\[
y = 3x + 18
\]

### **Final Answer**
The equation of the line is:

\[
y = 3x + 18
\]

Would you like a more detailed explanation?  

### **Related Questions:**
1. How do you convert a linear equation to standard form?
2. How do you find the equation of a line given one point and the slope?
3. What is the geometric meaning of the slope of a line?
4. How do parallel and perpendicular slopes relate?
5. How do you graph a line given its equation?

**Tip:** Always double-check the slope calculation to avoid mistakes when finding the equation of a line.

What is an equation of the line that passes through the points (−4, 6) and (−2, 0)?

Learn how to find the equation of a line passing through the points (−4, 6) and (−2, 0) using the point-slope formula and slope-intercept form. This step-by-step guide is perfect for Grades 7-9 students studying linear equations and slope.

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