Question

What is the equation of the line in standard form?



Responses

4x + y = -7
4x + y = -7

4x - y = 7
4x - y = 7

-3x + 5y = 3
-3x + 5 y = 3

-x - 3y = 5


The graph shows at the top (-3,5) over where the postive y line is and at the bottom (-1,-3) at the bottom is very the y line is but going down

Answer 1

To determine the equation of the line in standard form, we'll first identify the key points you provided: (-3, 5) and (-1, -3). Next, we can follow these steps:

1. **Find the slope (m)**: The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
With points (-3, 5) and (-1, -3):
\[
m = \frac{-3 - 5}{-1 - (-3)} = \frac{-8}{-1 + 3} = \frac{-8}{2} = -4
\]

2. **Use point-slope form**: The point-slope form of the linear equation is:
\[
y - y_1 = m(x - x_1)
\]
Using one of the points, (-3, 5):
\[
y - 5 = -4(x + 3)
\]

3. **Convert to standard form**: First, simplify the equation:
\[
y - 5 = -4x - 12
\]
Bringing y to the left:
\[
y = -4x - 7
\]
Now, move everything to one side to get it into standard form (Ax + By = C):
\[
4x + y = -7
\]

So the equation of the line in standard form is:

**4x + y = -7**.

Among the responses you provided, that matches the first option.