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To solve this problem, we need to find the equation of the line passing through the points \((2, -5)\) and \((-3, 10)\). Here's how we can do that:

### Step 1: Find the slope \( m \)
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute \((x_1, y_1) = (2, -5)\) and \((x_2, y_2) = (-3, 10)\):
\[
m = \frac{10 - (-5)}{-3 - 2} = \frac{10 + 5}{-5} = \frac{15}{-5} = -3
\]
So, the slope \( m = -3 \).

### Step 2: Use the point-slope form of a line
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
We can use one of the points, say \((2, -5)\), and the slope \(m = -3\):
\[
y - (-5) = -3(x - 2)
\]
Simplify:
\[
y + 5 = -3(x - 2)
\]
Distribute the \(-3\):
\[
y + 5 = -3x + 6
\]
Subtract 5 from both sides:
\[
y = -3x + 1
\]
This is the equation of the line in slope-intercept form.

### Step 3: Convert to standard form
To write the equation in standard form \(Ax + By = C\), we rearrange:
\[
y = -3x + 1
\]
Move the \(3x\) to the other side:
\[
3x + y = 1
\]

### Step 4: Check the options
The equation \(3x + y = 1\) matches **option B**.

Thus, the correct answer is **B: \(3x + y = 1\)**.

Do you want more details on any step or have any questions?

Here are 5 related questions:
1. How do you convert from slope-intercept form to standard form?


What is the equation in standard form of the line containing the points (2,-5) and (-3,10)?

Learn how to determine the equation of a line passing through the points (2,-5) and (-3,10) using slope-intercept and standard form. This problem covers key geometric concepts, including finding slopes and converting to standard form.

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