Find the equation of the line with  
m
=
−
2
  that passes through the point  
(
−
1
,
5
)
 .
Write your answer in standard form  
A
x
+
B
y
=
C
 .

To find the equation of the line in standard form \(Ax + By = C\), given the slope \(m = -2\) and a point \((-1, 5)\) on the line, follow these steps:

### Step 1: Use the point-slope form of the equation of a line
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

Substituting the given values:
\[
y - 5 = -2(x + 1)
\]

### Step 2: Simplify and expand the equation
Expand the equation to simplify it:
\[
y - 5 = -2x - 2
\]

Next, add 5 to both sides to isolate \(y\):
\[
y = -2x + 3
\]

### Step 3: Convert to standard form \(Ax + By = C\)
To convert the equation \(y = -2x + 3\) to standard form, rearrange it:
\[
2x + y = 3
\]

So, the equation in standard form is:
\[
\boxed{2x + y = 3}
\]

Would you like more details or have any questions about the process? Here are some additional questions related to this problem:

1. How would the equation change if the slope was positive instead of negative?
2. What is the significance of the slope in the context of the line's direction?
3. How would you find the x-intercept and y-intercept from the standard form equation?
4. Can you derive the slope from the standard form equation?
5. How do you convert a line equation from standard form to slope-intercept form?

**Tip:** When converting an equation to standard form, always try to ensure that the coefficients of \(x\) and \(y\) are integers, and the coefficient of \(x\) is positive.

Learn how to find the equation of a line with a slope of -2 passing through the point (-1, 5). Step-by-step solution provided in standard form Ax + By = C. Includes explanations on converting point-slope form to standard form and understanding the significance of slope in line equations. Suitable for Grades 7-9.

Math Problem Statement

Find the equation of the line with
m

− 2 that passes through the point
( − 1 , 5 ) . Write your answer in standard form
A x + B y

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